(8x+5)(4x-17)=180

Solution for (8x+5)(4x-17)=180 equation:

(8x+5)(4x-17)=180

We move all terms to the left:

(8x+5)(4x-17)-(180)=0

We multiply parentheses ..

(+32x^2-136x+20x-85)-180=0

We get rid of parentheses

32x^2-136x+20x-85-180=0

We add all the numbers together, and all the variables

32x^2-116x-265=0

a = 32; b = -116; c = -265;
Δ = b2-4ac
Δ = -1162-4·32·(-265)
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{-(-116)-12\sqrt{329}}{2*32}=\frac{116-12\sqrt{329}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-116)+12\sqrt{329}}{2*32}=\frac{116+12\sqrt{329}}{64}
$