(4x+8)(3x+12)=90

Solution for (4x+8)(3x+12)=90 equation:

(4x+8)(3x+12)=90

We move all terms to the left:

(4x+8)(3x+12)-(90)=0

We multiply parentheses ..

(+12x^2+48x+24x+96)-90=0

We get rid of parentheses

12x^2+48x+24x+96-90=0

We add all the numbers together, and all the variables

12x^2+72x+6=0

a = 12; b = 72; c = +6;
Δ = b2-4ac
Δ = 722-4·12·6
Δ = 4896
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:

$\sqrt{\Delta}=\sqrt{4896}=\sqrt{144*34}=\sqrt{144}*\sqrt{34}=12\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-12\sqrt{34}}{2*12}=\frac{-72-12\sqrt{34}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+12\sqrt{34}}{2*12}=\frac{-72+12\sqrt{34}}{24}
$