6x(3x+9)=90

Solution for 6x(3x+9)=90 equation:

6x(3x+9)=90

We move all terms to the left:

6x(3x+9)-(90)=0

We multiply parentheses

18x^2+54x-90=0

a = 18; b = 54; c = -90;
Δ = b2-4ac
Δ = 542-4·18·(-90)
Δ = 9396
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:

$\sqrt{\Delta}=\sqrt{9396}=\sqrt{324*29}=\sqrt{324}*\sqrt{29}=18\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-18\sqrt{29}}{2*18}=\frac{-54-18\sqrt{29}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+18\sqrt{29}}{2*18}=\frac{-54+18\sqrt{29}}{36}
$