(12x+3)(6x-3)=90

Solution for (12x+3)(6x-3)=90 equation:

(12x+3)(6x-3)=90

We move all terms to the left:

(12x+3)(6x-3)-(90)=0

We multiply parentheses ..

(+72x^2-36x+18x-9)-90=0

We get rid of parentheses

72x^2-36x+18x-9-90=0

We add all the numbers together, and all the variables

72x^2-18x-99=0

a = 72; b = -18; c = -99;
Δ = b2-4ac
Δ = -182-4·72·(-99)
Δ = 28836
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:

$\sqrt{\Delta}=\sqrt{28836}=\sqrt{324*89}=\sqrt{324}*\sqrt{89}=18\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18\sqrt{89}}{2*72}=\frac{18-18\sqrt{89}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18\sqrt{89}}{2*72}=\frac{18+18\sqrt{89}}{144}
$