(12x+9)x=90

Solution for (12x+9)x=90 equation:

(12x+9)x=90

We move all terms to the left:

(12x+9)x-(90)=0

We multiply parentheses

12x^2+9x-90=0

a = 12; b = 9; c = -90;
Δ = b2-4ac
Δ = 92-4·12·(-90)
Δ = 4401
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:

$\sqrt{\Delta}=\sqrt{4401}=\sqrt{9*489}=\sqrt{9}*\sqrt{489}=3\sqrt{489}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{489}}{2*12}=\frac{-9-3\sqrt{489}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{489}}{2*12}=\frac{-9+3\sqrt{489}}{24}
$