(20x+5)(24x-1)=360

Solution for (20x+5)(24x-1)=360 equation:

(20x+5)(24x-1)=360

We move all terms to the left:

(20x+5)(24x-1)-(360)=0

We multiply parentheses ..

(+480x^2-20x+120x-5)-360=0

We get rid of parentheses

480x^2-20x+120x-5-360=0

We add all the numbers together, and all the variables

480x^2+100x-365=0

a = 480; b = 100; c = -365;
Δ = b2-4ac
Δ = 1002-4·480·(-365)
Δ = 710800
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:

$\sqrt{\Delta}=\sqrt{710800}=\sqrt{400*1777}=\sqrt{400}*\sqrt{1777}=20\sqrt{1777}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20\sqrt{1777}}{2*480}=\frac{-100-20\sqrt{1777}}{960}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20\sqrt{1777}}{2*480}=\frac{-100+20\sqrt{1777}}{960}
$