(x+5)(2x+10)=90

Solution for (x+5)(2x+10)=90 equation:

(x+5)(2x+10)=90

We move all terms to the left:

(x+5)(2x+10)-(90)=0

We multiply parentheses ..

(+2x^2+10x+10x+50)-90=0

We get rid of parentheses

2x^2+10x+10x+50-90=0

We add all the numbers together, and all the variables

2x^2+20x-40=0

a = 2; b = 20; c = -40;
Δ = b2-4ac
Δ = 202-4·2·(-40)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-12\sqrt{5}}{2*2}=\frac{-20-12\sqrt{5}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+12\sqrt{5}}{2*2}=\frac{-20+12\sqrt{5}}{4}
$