(X+3)(4x-8)=90

Solution for (X+3)(4x-8)=90 equation:

(X+3)(4X-8)=90

We move all terms to the left:

(X+3)(4X-8)-(90)=0

We multiply parentheses ..

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

We get rid of parentheses

4X^2-8X+12X-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}
$