4x(3x+12)=90

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

4x(3x+12)=90

We move all terms to the left:

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

We multiply parentheses

12x^2+48x-90=0

a = 12; b = 48; c = -90;
Δ = b2-4ac
Δ = 482-4·12·(-90)
Δ = 6624
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:

$\sqrt{\Delta}=\sqrt{6624}=\sqrt{144*46}=\sqrt{144}*\sqrt{46}=12\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-12\sqrt{46}}{2*12}=\frac{-48-12\sqrt{46}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+12\sqrt{46}}{2*12}=\frac{-48+12\sqrt{46}}{24}
$