(x+4)(2x+10)=220

Solution for (x+4)(2x+10)=220 equation:

(x+4)(2x+10)=220

We move all terms to the left:

(x+4)(2x+10)-(220)=0

We multiply parentheses ..

(+2x^2+10x+8x+40)-220=0

We get rid of parentheses

2x^2+10x+8x+40-220=0

We add all the numbers together, and all the variables

2x^2+18x-180=0

a = 2; b = 18; c = -180;
Δ = b2-4ac
Δ = 182-4·2·(-180)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-42}{2*2}=\frac{-60}{4}
=-15$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+42}{2*2}=\frac{24}{4}
=6$