x(3x+12)=90

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

x(3x+12)=90

We move all terms to the left:

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

We multiply parentheses

3x^2+12x-90=0

a = 3; b = 12; c = -90;
Δ = b2-4ac
Δ = 122-4·3·(-90)
Δ = 1224
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:

$\sqrt{\Delta}=\sqrt{1224}=\sqrt{36*34}=\sqrt{36}*\sqrt{34}=6\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{34}}{2*3}=\frac{-12-6\sqrt{34}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{34}}{2*3}=\frac{-12+6\sqrt{34}}{6}
$