90+x(2x-20)+(x+10)=360

Solution for 90+x(2x-20)+(x+10)=360 equation:

90+x(2x-20)+(x+10)=360

We move all terms to the left:

90+x(2x-20)+(x+10)-(360)=0

We add all the numbers together, and all the variables

x(2x-20)+(x+10)-270=0

We multiply parentheses

2x^2-20x+(x+10)-270=0

We get rid of parentheses

2x^2-20x+x+10-270=0

We add all the numbers together, and all the variables

2x^2-19x-260=0

a = 2; b = -19; c = -260;
Δ = b2-4ac
Δ = -192-4·2·(-260)
Δ = 2441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{2441}}{2*2}=\frac{19-\sqrt{2441}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{2441}}{2*2}=\frac{19+\sqrt{2441}}{4}
$