(3x+2)(2x+18)=90

Solution for (3x+2)(2x+18)=90 equation:

(3x+2)(2x+18)=90

We move all terms to the left:

(3x+2)(2x+18)-(90)=0

We multiply parentheses ..

(+6x^2+54x+4x+36)-90=0

We get rid of parentheses

6x^2+54x+4x+36-90=0

We add all the numbers together, and all the variables

6x^2+58x-54=0

a = 6; b = 58; c = -54;
Δ = b2-4ac
Δ = 582-4·6·(-54)
Δ = 4660
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:

$\sqrt{\Delta}=\sqrt{4660}=\sqrt{4*1165}=\sqrt{4}*\sqrt{1165}=2\sqrt{1165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-2\sqrt{1165}}{2*6}=\frac{-58-2\sqrt{1165}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+2\sqrt{1165}}{2*6}=\frac{-58+2\sqrt{1165}}{12}
$