4x(3x+6)=90

Solution for 4x(3x+6)=90 equation:

4x(3x+6)=90

We move all terms to the left:

4x(3x+6)-(90)=0

We multiply parentheses

12x^2+24x-90=0

a = 12; b = 24; c = -90;
Δ = b2-4ac
Δ = 242-4·12·(-90)
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{-(24)-12\sqrt{34}}{2*12}=\frac{-24-12\sqrt{34}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12\sqrt{34}}{2*12}=\frac{-24+12\sqrt{34}}{24}
$