x(6+3x)=90

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

x(6+3x)=90

We move all terms to the left:

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

We add all the numbers together, and all the variables

x(3x+6)-90=0

We multiply parentheses

3x^2+6x-90=0

a = 3; b = 6; c = -90;
Δ = b2-4ac
Δ = 62-4·3·(-90)
Δ = 1116
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:

$\sqrt{\Delta}=\sqrt{1116}=\sqrt{36*31}=\sqrt{36}*\sqrt{31}=6\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{31}}{2*3}=\frac{-6-6\sqrt{31}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{31}}{2*3}=\frac{-6+6\sqrt{31}}{6}
$