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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+3x^2+5x-27x-45)-180=0

We get rid of parentheses

3x^2+5x-27x-45-180=0

We add all the numbers together, and all the variables

3x^2-22x-225=0

a = 3; b = -22; c = -225;
Δ = b2-4ac
Δ = -222-4·3·(-225)
Δ = 3184
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:

$\sqrt{\Delta}=\sqrt{3184}=\sqrt{16*199}=\sqrt{16}*\sqrt{199}=4\sqrt{199}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-4\sqrt{199}}{2*3}=\frac{22-4\sqrt{199}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+4\sqrt{199}}{2*3}=\frac{22+4\sqrt{199}}{6}
$