2x(x+1)=220

Solution for 2x(x+1)=220 equation:

2x(x+1)=220

We move all terms to the left:

2x(x+1)-(220)=0

We multiply parentheses

2x^2+2x-220=0

a = 2; b = 2; c = -220;
Δ = b2-4ac
Δ = 22-4·2·(-220)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-42}{2*2}=\frac{-44}{4}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+42}{2*2}=\frac{40}{4}
=10
$