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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+5x^2-4x-40x+32)-180=0

We get rid of parentheses

5x^2-4x-40x+32-180=0

We add all the numbers together, and all the variables

5x^2-44x-148=0

a = 5; b = -44; c = -148;
Δ = b2-4ac
Δ = -442-4·5·(-148)
Δ = 4896
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:

$\sqrt{\Delta}=\sqrt{4896}=\sqrt{144*34}=\sqrt{144}*\sqrt{34}=12\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-12\sqrt{34}}{2*5}=\frac{44-12\sqrt{34}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+12\sqrt{34}}{2*5}=\frac{44+12\sqrt{34}}{10}
$