2(x-5)+x(x-10)=360

Solution for 2(x-5)+x(x-10)=360 equation:

2(x-5)+x(x-10)=360

We move all terms to the left:

2(x-5)+x(x-10)-(360)=0

We multiply parentheses

x^2+2x-10x-10-360=0

We add all the numbers together, and all the variables

x^2-8x-370=0

a = 1; b = -8; c = -370;
Δ = b2-4ac
Δ = -82-4·1·(-370)
Δ = 1544
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:

$\sqrt{\Delta}=\sqrt{1544}=\sqrt{4*386}=\sqrt{4}*\sqrt{386}=2\sqrt{386}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{386}}{2*1}=\frac{8-2\sqrt{386}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{386}}{2*1}=\frac{8+2\sqrt{386}}{2}
$