(8x-5)(4x-19)=180

Solution for (8x-5)(4x-19)=180 equation:

(8x-5)(4x-19)=180

We move all terms to the left:

(8x-5)(4x-19)-(180)=0

We multiply parentheses ..

(+32x^2-152x-20x+95)-180=0

We get rid of parentheses

32x^2-152x-20x+95-180=0

We add all the numbers together, and all the variables

32x^2-172x-85=0

a = 32; b = -172; c = -85;
Δ = b2-4ac
Δ = -1722-4·32·(-85)
Δ = 40464
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:

$\sqrt{\Delta}=\sqrt{40464}=\sqrt{144*281}=\sqrt{144}*\sqrt{281}=12\sqrt{281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-172)-12\sqrt{281}}{2*32}=\frac{172-12\sqrt{281}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-172)+12\sqrt{281}}{2*32}=\frac{172+12\sqrt{281}}{64}
$