x(x-10)+(x+30)+2x=360

Solution for x(x-10)+(x+30)+2x=360 equation:

x(x-10)+(x+30)+2x=360

We move all terms to the left:

x(x-10)+(x+30)+2x-(360)=0

We add all the numbers together, and all the variables

2x+x(x-10)+(x+30)-360=0

We multiply parentheses

x^2+2x-10x+(x+30)-360=0

We get rid of parentheses

x^2+2x-10x+x+30-360=0

We add all the numbers together, and all the variables

x^2-7x-330=0

a = 1; b = -7; c = -330;
Δ = b2-4ac
Δ = -72-4·1·(-330)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-37}{2*1}=\frac{-30}{2}
=-15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+37}{2*1}=\frac{44}{2}
=22
$