(2x-5)(x-5)=(2x-11)(2x+5)

Solution for (2x-5)(x-5)=(2x-11)(2x+5) equation:

(2x-5)(x-5)=(2x-11)(2x+5)

We move all terms to the left:

(2x-5)(x-5)-((2x-11)(2x+5))=0

We multiply parentheses ..

(+2x^2-10x-5x+25)-((2x-11)(2x+5))=0


We calculate terms in parentheses: -((2x-11)(2x+5)), so:

(2x-11)(2x+5)

We multiply parentheses ..

(+4x^2+10x-22x-55)

We get rid of parentheses

4x^2+10x-22x-55

We add all the numbers together, and all the variables

4x^2-12x-55

Back to the equation:

-(4x^2-12x-55)


We get rid of parentheses

2x^2-4x^2-10x-5x+12x+25+55=0

We add all the numbers together, and all the variables

-2x^2-3x+80=0

a = -2; b = -3; c = +80;
Δ = b2-4ac
Δ = -32-4·(-2)·80
Δ = 649
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{-(-3)-\sqrt{649}}{2*-2}=\frac{3-\sqrt{649}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{649}}{2*-2}=\frac{3+\sqrt{649}}{-4}
$