(6x-24)(4x-15)=180

Solution for (6x-24)(4x-15)=180 equation:

(6x-24)(4x-15)=180

We move all terms to the left:

(6x-24)(4x-15)-(180)=0

We multiply parentheses ..

(+24x^2-90x-96x+360)-180=0

We get rid of parentheses

24x^2-90x-96x+360-180=0

We add all the numbers together, and all the variables

24x^2-186x+180=0

a = 24; b = -186; c = +180;
Δ = b2-4ac
Δ = -1862-4·24·180
Δ = 17316
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:

$\sqrt{\Delta}=\sqrt{17316}=\sqrt{36*481}=\sqrt{36}*\sqrt{481}=6\sqrt{481}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-186)-6\sqrt{481}}{2*24}=\frac{186-6\sqrt{481}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-186)+6\sqrt{481}}{2*24}=\frac{186+6\sqrt{481}}{48}
$