(2x+12)(x+18)=90

Solution for (2x+12)(x+18)=90 equation:

(2x+12)(x+18)=90

We move all terms to the left:

(2x+12)(x+18)-(90)=0

We multiply parentheses ..

(+2x^2+36x+12x+216)-90=0

We get rid of parentheses

2x^2+36x+12x+216-90=0

We add all the numbers together, and all the variables

2x^2+48x+126=0

a = 2; b = 48; c = +126;
Δ = b2-4ac
Δ = 482-4·2·126
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-36}{2*2}=\frac{-84}{4}
=-21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+36}{2*2}=\frac{-12}{4}
=-3
$