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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-8x-190=0

a = 1; b = -8; c = -190;
Δ = b2-4ac
Δ = -82-4·1·(-190)
Δ = 824
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:

$\sqrt{\Delta}=\sqrt{824}=\sqrt{4*206}=\sqrt{4}*\sqrt{206}=2\sqrt{206}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{206}}{2*1}=\frac{8-2\sqrt{206}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{206}}{2*1}=\frac{8+2\sqrt{206}}{2}
$