x^2+(5x-6)(5x-6)=20

Solution for x^2+(5x-6)(5x-6)=20 equation:

x^2+(5x-6)(5x-6)=20

We move all terms to the left:

x^2+(5x-6)(5x-6)-(20)=0

We multiply parentheses ..

x^2+(+25x^2-30x-30x+36)-20=0

We get rid of parentheses

x^2+25x^2-30x-30x+36-20=0

We add all the numbers together, and all the variables

26x^2-60x+16=0

a = 26; b = -60; c = +16;
Δ = b2-4ac
Δ = -602-4·26·16
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-44}{2*26}=\frac{16}{52}
=4/13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+44}{2*26}=\frac{104}{52}
=2
$