x/(2x-5)=2x+5

Solution for x/(2x-5)=2x+5 equation:

x/(2x-5)=2x+5

We move all terms to the left:

x/(2x-5)-(2x+5)=0


Domain of the equation: (2x-5)!=0

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

2x!=5

x!=5/2

x!=2+1/2

x∈R


We get rid of parentheses

x/(2x-5)-2x-5=0

We multiply all the terms by the denominator


x-2x*(2x-5)-5*(2x-5)=0

We multiply parentheses

-4x^2+x+10x-10x+25=0

We add all the numbers together, and all the variables

-4x^2+x+25=0

a = -4; b = 1; c = +25;
Δ = b2-4ac
Δ = 12-4·(-4)·25
Δ = 401
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{-(1)-\sqrt{401}}{2*-4}=\frac{-1-\sqrt{401}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{401}}{2*-4}=\frac{-1+\sqrt{401}}{-8}
$