(5x+3)(9x-33)=180

Solution for (5x+3)(9x-33)=180 equation:

(5x+3)(9x-33)=180

We move all terms to the left:

(5x+3)(9x-33)-(180)=0

We multiply parentheses ..

(+45x^2-165x+27x-99)-180=0

We get rid of parentheses

45x^2-165x+27x-99-180=0

We add all the numbers together, and all the variables

45x^2-138x-279=0

a = 45; b = -138; c = -279;
Δ = b2-4ac
Δ = -1382-4·45·(-279)
Δ = 69264
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:

$\sqrt{\Delta}=\sqrt{69264}=\sqrt{144*481}=\sqrt{144}*\sqrt{481}=12\sqrt{481}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-138)-12\sqrt{481}}{2*45}=\frac{138-12\sqrt{481}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-138)+12\sqrt{481}}{2*45}=\frac{138+12\sqrt{481}}{90}
$