(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+12x-190=0

a = 1; b = 12; c = -190;
Δ = b2-4ac
Δ = 122-4·1·(-190)
Δ = 904
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:

$\sqrt{\Delta}=\sqrt{904}=\sqrt{4*226}=\sqrt{4}*\sqrt{226}=2\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{226}}{2*1}=\frac{-12-2\sqrt{226}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{226}}{2*1}=\frac{-12+2\sqrt{226}}{2}
$