(5x+3)(9x-33)=90

Solution for (5x+3)(9x-33)=90 equation:

(5x+3)(9x-33)=90

We move all terms to the left:

(5x+3)(9x-33)-(90)=0

We multiply parentheses ..

(+45x^2-165x+27x-99)-90=0

We get rid of parentheses

45x^2-165x+27x-99-90=0

We add all the numbers together, and all the variables

45x^2-138x-189=0

a = 45; b = -138; c = -189;
Δ = b2-4ac
Δ = -1382-4·45·(-189)
Δ = 53064
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:

$\sqrt{\Delta}=\sqrt{53064}=\sqrt{36*1474}=\sqrt{36}*\sqrt{1474}=6\sqrt{1474}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-138)-6\sqrt{1474}}{2*45}=\frac{138-6\sqrt{1474}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-138)+6\sqrt{1474}}{2*45}=\frac{138+6\sqrt{1474}}{90}
$