(5x+9)(9x-3)=180

Solution for (5x+9)(9x-3)=180 equation:

(5x+9)(9x-3)=180

We move all terms to the left:

(5x+9)(9x-3)-(180)=0

We multiply parentheses ..

(+45x^2-15x+81x-27)-180=0

We get rid of parentheses

45x^2-15x+81x-27-180=0

We add all the numbers together, and all the variables

45x^2+66x-207=0

a = 45; b = 66; c = -207;
Δ = b2-4ac
Δ = 662-4·45·(-207)
Δ = 41616
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{41616}=204$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-204}{2*45}=\frac{-270}{90}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+204}{2*45}=\frac{138}{90}
=1+8/15
$