(x-5)(x-6)=120

Solution for (x-5)(x-6)=120 equation:

(x-5)(x-6)=120

We move all terms to the left:

(x-5)(x-6)-(120)=0

We multiply parentheses ..

(+x^2-6x-5x+30)-120=0

We get rid of parentheses

x^2-6x-5x+30-120=0

We add all the numbers together, and all the variables

x^2-11x-90=0

a = 1; b = -11; c = -90;
Δ = b2-4ac
Δ = -112-4·1·(-90)
Δ = 481
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{-(-11)-\sqrt{481}}{2*1}=\frac{11-\sqrt{481}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{481}}{2*1}=\frac{11+\sqrt{481}}{2}
$