(3x+8)(5x-40)=180

Solution for (3x+8)(5x-40)=180 equation:

(3x+8)(5x-40)=180

We move all terms to the left:

(3x+8)(5x-40)-(180)=0

We multiply parentheses ..

(+15x^2-120x+40x-320)-180=0

We get rid of parentheses

15x^2-120x+40x-320-180=0

We add all the numbers together, and all the variables

15x^2-80x-500=0

a = 15; b = -80; c = -500;
Δ = b2-4ac
Δ = -802-4·15·(-500)
Δ = 36400
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:

$\sqrt{\Delta}=\sqrt{36400}=\sqrt{400*91}=\sqrt{400}*\sqrt{91}=20\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-20\sqrt{91}}{2*15}=\frac{80-20\sqrt{91}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+20\sqrt{91}}{2*15}=\frac{80+20\sqrt{91}}{30}
$