(9x)(5x+6)=90

Solution for (9x)(5x+6)=90 equation:

(9x)(5x+6)=90

We move all terms to the left:

(9x)(5x+6)-(90)=0

We multiply parentheses

45x^2+54x-90=0

a = 45; b = 54; c = -90;
Δ = b2-4ac
Δ = 542-4·45·(-90)
Δ = 19116
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:

$\sqrt{\Delta}=\sqrt{19116}=\sqrt{324*59}=\sqrt{324}*\sqrt{59}=18\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-18\sqrt{59}}{2*45}=\frac{-54-18\sqrt{59}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+18\sqrt{59}}{2*45}=\frac{-54+18\sqrt{59}}{90}
$