(2x-1)/(4x-7)=x

Solution for (2x-1)/(4x-7)=x equation:

(2x-1)/(4x-7)=x

We move all terms to the left:

(2x-1)/(4x-7)-(x)=0


Domain of the equation: (4x-7)!=0

We move all terms containing x to the left, all other terms to the right

4x!=7

x!=7/4

x!=1+3/4

x∈R


We add all the numbers together, and all the variables

-1x+(2x-1)/(4x-7)=0

We multiply all the terms by the denominator


-1x*(4x-7)+(2x-1)=0

We multiply parentheses

-4x^2+7x+(2x-1)=0

We get rid of parentheses

-4x^2+7x+2x-1=0

We add all the numbers together, and all the variables

-4x^2+9x-1=0

a = -4; b = 9; c = -1;
Δ = b2-4ac
Δ = 92-4·(-4)·(-1)
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{65}}{2*-4}=\frac{-9-\sqrt{65}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{65}}{2*-4}=\frac{-9+\sqrt{65}}{-8}
$