(5x+9)(8x-30)=180

Solution for (5x+9)(8x-30)=180 equation:

(5x+9)(8x-30)=180

We move all terms to the left:

(5x+9)(8x-30)-(180)=0

We multiply parentheses ..

(+40x^2-150x+72x-270)-180=0

We get rid of parentheses

40x^2-150x+72x-270-180=0

We add all the numbers together, and all the variables

40x^2-78x-450=0

a = 40; b = -78; c = -450;
Δ = b2-4ac
Δ = -782-4·40·(-450)
Δ = 78084
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:

$\sqrt{\Delta}=\sqrt{78084}=\sqrt{324*241}=\sqrt{324}*\sqrt{241}=18\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-18\sqrt{241}}{2*40}=\frac{78-18\sqrt{241}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+18\sqrt{241}}{2*40}=\frac{78+18\sqrt{241}}{80}
$