x(2x+12)=90

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

x(2x+12)=90

We move all terms to the left:

x(2x+12)-(90)=0

We multiply parentheses

2x^2+12x-90=0

a = 2; b = 12; c = -90;
Δ = b2-4ac
Δ = 122-4·2·(-90)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{6}}{2*2}=\frac{-12-12\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{6}}{2*2}=\frac{-12+12\sqrt{6}}{4}
$