(2x+12)(3x-18)=90

Solution for (2x+12)(3x-18)=90 equation:

(2x+12)(3x-18)=90

We move all terms to the left:

(2x+12)(3x-18)-(90)=0

We multiply parentheses ..

(+6x^2-36x+36x-216)-90=0

We get rid of parentheses

6x^2-36x+36x-216-90=0

We add all the numbers together, and all the variables

6x^2-306=0

a = 6; b = 0; c = -306;
Δ = b2-4ac
Δ = 02-4·6·(-306)
Δ = 7344
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:

$\sqrt{\Delta}=\sqrt{7344}=\sqrt{144*51}=\sqrt{144}*\sqrt{51}=12\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{51}}{2*6}=\frac{0-12\sqrt{51}}{12}
=-\frac{12\sqrt{51}}{12}
=-\sqrt{51}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{51}}{2*6}=\frac{0+12\sqrt{51}}{12}
=\frac{12\sqrt{51}}{12}
=\sqrt{51}
$