(2x-5)(2x-5)-(x-6)(x-6)-80=0

Solution for (2x-5)(2x-5)-(x-6)(x-6)-80=0 equation:

(2x-5)(2x-5)-(x-6)(x-6)-80=0

We multiply parentheses ..

(+4x^2-10x-10x+25)-(x-6)(x-6)-80=0

We get rid of parentheses

4x^2-10x-10x-(x-6)(x-6)+25-80=0

We multiply parentheses ..

4x^2-(+x^2-6x-6x+36)-10x-10x+25-80=0

We add all the numbers together, and all the variables

4x^2-(+x^2-6x-6x+36)-20x-55=0

We get rid of parentheses

4x^2-x^2+6x+6x-20x-36-55=0

We add all the numbers together, and all the variables

3x^2-8x-91=0

a = 3; b = -8; c = -91;
Δ = b2-4ac
Δ = -82-4·3·(-91)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-34}{2*3}=\frac{-26}{6}
=-4+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+34}{2*3}=\frac{42}{6}
=7
$