(2x-2)(x-5)=110

Solution for (2x-2)(x-5)=110 equation:

(2x-2)(x-5)=110

We move all terms to the left:

(2x-2)(x-5)-(110)=0

We multiply parentheses ..

(+2x^2-10x-2x+10)-110=0

We get rid of parentheses

2x^2-10x-2x+10-110=0

We add all the numbers together, and all the variables

2x^2-12x-100=0

a = 2; b = -12; c = -100;
Δ = b2-4ac
Δ = -122-4·2·(-100)
Δ = 944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{944}=\sqrt{16*59}=\sqrt{16}*\sqrt{59}=4\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{59}}{2*2}=\frac{12-4\sqrt{59}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{59}}{2*2}=\frac{12+4\sqrt{59}}{4}
$