(X+2)(4x-12)=90

Solution for (X+2)(4x-12)=90 equation:

(X+2)(4X-12)=90

We move all terms to the left:

(X+2)(4X-12)-(90)=0

We multiply parentheses ..

(+4X^2-12X+8X-24)-90=0

We get rid of parentheses

4X^2-12X+8X-24-90=0

We add all the numbers together, and all the variables

4X^2-4X-114=0

a = 4; b = -4; c = -114;
Δ = b2-4ac
Δ = -42-4·4·(-114)
Δ = 1840
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:

$\sqrt{\Delta}=\sqrt{1840}=\sqrt{16*115}=\sqrt{16}*\sqrt{115}=4\sqrt{115}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{115}}{2*4}=\frac{4-4\sqrt{115}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{115}}{2*4}=\frac{4+4\sqrt{115}}{8}
$