(9x-17)(4x+28)=180

Solution for (9x-17)(4x+28)=180 equation:

(9x-17)(4x+28)=180

We move all terms to the left:

(9x-17)(4x+28)-(180)=0

We multiply parentheses ..

(+36x^2+252x-68x-476)-180=0

We get rid of parentheses

36x^2+252x-68x-476-180=0

We add all the numbers together, and all the variables

36x^2+184x-656=0

a = 36; b = 184; c = -656;
Δ = b2-4ac
Δ = 1842-4·36·(-656)
Δ = 128320
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:

$\sqrt{\Delta}=\sqrt{128320}=\sqrt{64*2005}=\sqrt{64}*\sqrt{2005}=8\sqrt{2005}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(184)-8\sqrt{2005}}{2*36}=\frac{-184-8\sqrt{2005}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(184)+8\sqrt{2005}}{2*36}=\frac{-184+8\sqrt{2005}}{72}
$