115(x+17)(7x-16)=180

Solution for 115(x+17)(7x-16)=180 equation:

115(x+17)(7x-16)=180

We move all terms to the left:

115(x+17)(7x-16)-(180)=0

We multiply parentheses ..

115(+7x^2-16x+119x-272)-180=0

We multiply parentheses

805x^2-1840x+13685x-31280-180=0

We add all the numbers together, and all the variables

805x^2+11845x-31460=0

a = 805; b = 11845; c = -31460;
Δ = b2-4ac
Δ = 118452-4·805·(-31460)
Δ = 241605225
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:

$\sqrt{\Delta}=\sqrt{241605225}=\sqrt{225*1073801}=\sqrt{225}*\sqrt{1073801}=15\sqrt{1073801}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11845)-15\sqrt{1073801}}{2*805}=\frac{-11845-15\sqrt{1073801}}{1610}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11845)+15\sqrt{1073801}}{2*805}=\frac{-11845+15\sqrt{1073801}}{1610}
$