(8x-17)(4x+11)=180

Solution for (8x-17)(4x+11)=180 equation:

(8x-17)(4x+11)=180

We move all terms to the left:

(8x-17)(4x+11)-(180)=0

We multiply parentheses ..

(+32x^2+88x-68x-187)-180=0

We get rid of parentheses

32x^2+88x-68x-187-180=0

We add all the numbers together, and all the variables

32x^2+20x-367=0

a = 32; b = 20; c = -367;
Δ = b2-4ac
Δ = 202-4·32·(-367)
Δ = 47376
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:

$\sqrt{\Delta}=\sqrt{47376}=\sqrt{144*329}=\sqrt{144}*\sqrt{329}=12\sqrt{329}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-12\sqrt{329}}{2*32}=\frac{-20-12\sqrt{329}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+12\sqrt{329}}{2*32}=\frac{-20+12\sqrt{329}}{64}
$