120+120+120+100+x(x+10)=720

Solution for 120+120+120+100+x(x+10)=720 equation:

120+120+120+100+x(x+10)=720

We move all terms to the left:

120+120+120+100+x(x+10)-(720)=0

We add all the numbers together, and all the variables

x(x+10)-260=0

We multiply parentheses

x^2+10x-260=0

a = 1; b = 10; c = -260;
Δ = b2-4ac
Δ = 102-4·1·(-260)
Δ = 1140
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:

$\sqrt{\Delta}=\sqrt{1140}=\sqrt{4*285}=\sqrt{4}*\sqrt{285}=2\sqrt{285}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{285}}{2*1}=\frac{-10-2\sqrt{285}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{285}}{2*1}=\frac{-10+2\sqrt{285}}{2}
$