X+2x(x+20)+120=360

Solution for X+2x(x+20)+120=360 equation:

X+2X(X+20)+120=360

We move all terms to the left:

X+2X(X+20)+120-(360)=0

We add all the numbers together, and all the variables

X+2X(X+20)-240=0

We multiply parentheses

2X^2+X+40X-240=0

We add all the numbers together, and all the variables

2X^2+41X-240=0

a = 2; b = 41; c = -240;
Δ = b2-4ac
Δ = 412-4·2·(-240)
Δ = 3601
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{-(41)-\sqrt{3601}}{2*2}=\frac{-41-\sqrt{3601}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+\sqrt{3601}}{2*2}=\frac{-41+\sqrt{3601}}{4}
$