(8x-5)(5x+15)=40=180

Solution for (8x-5)(5x+15)=40=180 equation:

(8x-5)(5x+15)=40=180

We move all terms to the left:

(8x-5)(5x+15)-(40)=0

We multiply parentheses ..

(+40x^2+120x-25x-75)-40=0

We get rid of parentheses

40x^2+120x-25x-75-40=0

We add all the numbers together, and all the variables

40x^2+95x-115=0

a = 40; b = 95; c = -115;
Δ = b2-4ac
Δ = 952-4·40·(-115)
Δ = 27425
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:

$\sqrt{\Delta}=\sqrt{27425}=\sqrt{25*1097}=\sqrt{25}*\sqrt{1097}=5\sqrt{1097}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(95)-5\sqrt{1097}}{2*40}=\frac{-95-5\sqrt{1097}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(95)+5\sqrt{1097}}{2*40}=\frac{-95+5\sqrt{1097}}{80}
$