(3x+9)(2x-4)=90

Solution for (3x+9)(2x-4)=90 equation:

(3x+9)(2x-4)=90

We move all terms to the left:

(3x+9)(2x-4)-(90)=0

We multiply parentheses ..

(+6x^2-12x+18x-36)-90=0

We get rid of parentheses

6x^2-12x+18x-36-90=0

We add all the numbers together, and all the variables

6x^2+6x-126=0

a = 6; b = 6; c = -126;
Δ = b2-4ac
Δ = 62-4·6·(-126)
Δ = 3060
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:

$\sqrt{\Delta}=\sqrt{3060}=\sqrt{36*85}=\sqrt{36}*\sqrt{85}=6\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{85}}{2*6}=\frac{-6-6\sqrt{85}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{85}}{2*6}=\frac{-6+6\sqrt{85}}{12}
$