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On line Solution of Monovariate Equation：
    Input any unary equation directly, and then click the "Next" button to obtain the solution of the equation.
    It supports equations that contain mathematical functions.
    Current location：Equations > Monovariate Equation > The history of univariate equation calculation > Answer

    Overview: 1 questions will be solved this time.Among them
           ☆1 equations

[ 1/1 Equation]
    Work: Find the solution of equation 0.375/((1+0.952*x)*(1+0.952*x))-1/((1+1.051*1/x)*(1+1.051*1/x)) = 0.828*x .
    Question type: Equation
    Solution:Original question:
     
3
8
 ÷ ((1 +
119
125
 x )(1 +
119
125
 x )) − 1 ÷ ((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x )) =
207
250
 x
     Multiply both sides of the equation by:((1 +
119
125
 x )(1 +
119
125
 x ))
     
3
8
 − 1 ÷ ((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x )) × ((1 +
119
125
 x )(1 +
119
125
 x )) =
207
250
 x ((1 +
119
125
 x )(1 +
119
125
 x ))
    Remove a bracket on the left of the equation:：
     
3
8
 − 1 ÷ ((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x )) × (1 +
119
125
 x )(1 +
119
125
 x ) =
207
250
 x ((1 +
119
125
 x )(1 +
119
125
 x ))
    Remove a bracket on the right of the equation:：
     
3
8
 − 1 ÷ ((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x )) × (1 +
119
125
 x )(1 +
119
125
 x ) =
207
250
 x (1 +
119
125
 x )(1 +
119
125
 x )
     Multiply both sides of the equation by:((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x ))
     
3
8
((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x )) − 1(1 +
119
125
 x )(1 +
119
125
 x ) =
207
250
 x (1 +
119
125
 x )(1 +
119
125
 x )((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x ))
    Remove a bracket on the left of the equation:
     
3
8
(1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x ) − 1(1 +
119
125
 x )(1 +
119
125
 x ) =
207
250
 x (1 +
119
125
 x )(1 +
119
125
 x )((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x ))
    Remove a bracket on the right of the equation:：
     
3
8
(1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x ) − 1(1 +
119
125
 x )(1 +
119
125
 x ) =
207
250
 x × 1(1 +
119
125
 x )((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x )) +
207
250
 x ×
119
125
 x (1 +
119
125
 x )((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x ))
    The equation is reduced to :
     
3
8
(1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x ) − 1(1 +
119
125
 x )(1 +
119
125
 x ) =
207
250
 x (1 +
119
125
 x )((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x )) +
24633
31250
 x x (1 +
119
125
 x )((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x ))
    Remove a bracket on the left of the equation:
     
3
8
 × 1(1 +
1051
1000
 × 1 ÷ x ) +
3
8
 ×
1051
1000
 × 1 ÷ x × (1 +
1051
1000
 × 1 ÷ x ) − 1(1 +
119
125
 x )(1 +
119
125
 x ) =
207
250
 x (1 +
119
125
 x )((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x )) +
24633
31250
 x x (1 +
119
125
 x )((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x ))
    Remove a bracket on the right of the equation:：
     
3
8
 × 1(1 +
1051
1000
 × 1 ÷ x ) +
3
8
 ×
1051
1000
 × 1 ÷ x × (1 +
1051
1000
 × 1 ÷ x ) − 1(1 +
119
125
 x )(1 +
119
125
 x ) =
207
250
 x × 1((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x )) +
207
250
 x ×
119
125
 x ((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x )) +
24633
31250
 x x
    The equation is reduced to :
     
3
8
(1 +
1051
1000
 × 1 ÷ x ) +
3153
8000
 ÷ x × (1 +
1051
1000
 × 1 ÷ x ) − 1(1 +
119
125
 x )(1 +
119
125
 x ) =
207
250
 x ((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x )) +
24633
31250
 x x ((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x )) +
24633
31250
 x x (1 +
119
125
 x )((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x ))
     Multiply both sides of the equation by: x
     
3
8
(1 +
1051
1000
 × 1 ÷ x ) x +
3153
8000
(1 +
1051
1000
 × 1 ÷ x ) − 1(1 +
119
125
 x )(1 +
119
125
 x ) x =
207
250
 x ((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x )) x +
24633
31250
 x x ((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x )) x +
24633
31250
 x x
    Remove a bracket on the left of the equation:
     
3
8
 × 1 x +
3
8
 ×
1051
1000
 × 1 ÷ x × x +
3153
8000
(1 +
1051
1000
 × 1 ÷ x ) − 1(1 +
119
125
 x ) =
207
250
 x ((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x )) x +
24633
31250
 x x ((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x )) x +
24633
31250
 x x
    Remove a bracket on the right of the equation:：
     
3
8
 × 1 x +
3
8
 ×
1051
1000
 × 1 ÷ x × x +
3153
8000
(1 +
1051
1000
 × 1 ÷ x ) − 1(1 +
119
125
 x ) =
207
250
 x (1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x ) x +
24633
31250
 x x ((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x )) x +
24633
31250
 x
    The equation is reduced to :
     
3
8
 x +
3153
8000
 ÷ x × x +
3153
8000
(1 +
1051
1000
 × 1 ÷ x ) − 1(1 +
119
125
 x )(1 +
119
125
 x ) x =
207
250
 x (1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x ) x +
24633
31250
 x x ((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x )) x +
24633
31250
 x
    Remove a bracket on the left of the equation:
     
3
8
 x +
3153
8000
 ÷ 1 × 1 +
3153
8000
 × 1 +
3153
8000
 ×
1051
1000
 × 1 ÷ x − 1 =
207
250
 x (1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x ) x +
24633
31250
 x x ((1 +
1051
1000
 × 1 ÷ x )(1 +
1051
1000
 × 1 ÷ x )) x +
24633
31250
 x
    Remove a bracket on the right of the equation:：
     
3
8
 x +
3153
8000
 ÷ 1 × 1 +
3153
8000
 × 1 +
3153
8000
 ×
1051
1000
 × 1 ÷ x − 1 =
207
250
 x × 1(1 +
1051
1000
 × 1 ÷ x ) x +
207
250
 x ×
1051
1000
 × 1 ÷ x × (1 +
1051
1000
 × 1 ÷ x ) x
    The equation is reduced to :
     
3
8
 x +
3153
8000
 +
3153
8000
 +
3313803
8000000
 ÷ x − 1(1 +
119
125
 x )(1 +
119
125
 x ) x =
207
250
 x (1 +
1051
1000
 × 1 ÷ x ) x +
217557
250000
 x ÷ x × (1 +
1051
1000
 × 1 ÷ x ) x +
24633
31250
 x x
    The equation is reduced to :
     
3
8
 x +
3153
4000
 +
3313803
8000000
 ÷ x − 1(1 +
119
125
 x )(1 +
119
125
 x ) x =
207
250
 x (1 +
1051
1000
 × 1 ÷ x ) x +
217557
250000
 x ÷ x × (1 +
1051
1000
 × 1 ÷ x ) x +
24633
31250
 x x
     Multiply both sides of the equation by: x
     
3
8
 x x +
3153
4000
 x +
3313803
8000000
 − 1(1 +
119
125
 x )(1 +
119
125
 x ) x x =
207
250
 x (1 +
1051
1000
 × 1 ÷ x ) x x +
217557
250000
 × 1 ÷ 1 × (1 +
1051
1000
 × 1 ÷ x ) x x +
24633
31250
    Remove a bracket on the left of the equation:
     
3
8
 x x +
3153
4000
 x +
3313803
8000000
 − 1 × 1(1 +
119
125
 x ) x x − 1 =
207
250
 x (1 +
1051
1000
 × 1 ÷ x ) x x +
217557
250000
 × 1 ÷ 1 × (1 +
1051
1000
 × 1 ÷ x ) x x +
24633
31250
    Remove a bracket on the right of the equation:：
     
3
8
 x x +
3153
4000
 x +
3313803
8000000
 − 1 × 1(1 +
119
125
 x ) x x − 1 =
207
250
 x × 1 x x +
207
250
 x ×
1051
1000
 × 1 ÷ x × x x

    The solution of the equation:
        x1≈-2.862980 , keep 6 decimal places
        x2≈-0.697967 , keep 6 decimal places
        x3≈0.250520 , keep 6 decimal places    
    There are 3 solution(s).

解程的详细方法请参阅：《方程的解法》


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