x(2x+30)=220

Solution for x(2x+30)=220 equation:

x(2x+30)=220

We move all terms to the left:

x(2x+30)-(220)=0

We multiply parentheses

2x^2+30x-220=0

a = 2; b = 30; c = -220;
Δ = b2-4ac
Δ = 302-4·2·(-220)
Δ = 2660
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:

$\sqrt{\Delta}=\sqrt{2660}=\sqrt{4*665}=\sqrt{4}*\sqrt{665}=2\sqrt{665}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{665}}{2*2}=\frac{-30-2\sqrt{665}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{665}}{2*2}=\frac{-30+2\sqrt{665}}{4}
$