(5x+8)(6x-18)=180

Solution for (5x+8)(6x-18)=180 equation:

(5x+8)(6x-18)=180

We move all terms to the left:

(5x+8)(6x-18)-(180)=0

We multiply parentheses ..

(+30x^2-90x+48x-144)-180=0

We get rid of parentheses

30x^2-90x+48x-144-180=0

We add all the numbers together, and all the variables

30x^2-42x-324=0

a = 30; b = -42; c = -324;
Δ = b2-4ac
Δ = -422-4·30·(-324)
Δ = 40644
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:

$\sqrt{\Delta}=\sqrt{40644}=\sqrt{36*1129}=\sqrt{36}*\sqrt{1129}=6\sqrt{1129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{1129}}{2*30}=\frac{42-6\sqrt{1129}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{1129}}{2*30}=\frac{42+6\sqrt{1129}}{60}
$