(2x-10)(x-2)=180

Solution for (2x-10)(x-2)=180 equation:

(2x-10)(x-2)=180

We move all terms to the left:

(2x-10)(x-2)-(180)=0

We multiply parentheses ..

(+2x^2-4x-10x+20)-180=0

We get rid of parentheses

2x^2-4x-10x+20-180=0

We add all the numbers together, and all the variables

2x^2-14x-160=0

a = 2; b = -14; c = -160;
Δ = b2-4ac
Δ = -142-4·2·(-160)
Δ = 1476
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:

$\sqrt{\Delta}=\sqrt{1476}=\sqrt{36*41}=\sqrt{36}*\sqrt{41}=6\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6\sqrt{41}}{2*2}=\frac{14-6\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6\sqrt{41}}{2*2}=\frac{14+6\sqrt{41}}{4}
$