(2x+7)(3x-12)=90

Solution for (2x+7)(3x-12)=90 equation:

(2x+7)(3x-12)=90

We move all terms to the left:

(2x+7)(3x-12)-(90)=0

We multiply parentheses ..

(+6x^2-24x+21x-84)-90=0

We get rid of parentheses

6x^2-24x+21x-84-90=0

We add all the numbers together, and all the variables

6x^2-3x-174=0

a = 6; b = -3; c = -174;
Δ = b2-4ac
Δ = -32-4·6·(-174)
Δ = 4185
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:

$\sqrt{\Delta}=\sqrt{4185}=\sqrt{9*465}=\sqrt{9}*\sqrt{465}=3\sqrt{465}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{465}}{2*6}=\frac{3-3\sqrt{465}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{465}}{2*6}=\frac{3+3\sqrt{465}}{12}
$