(2x-33)(4x-163)=180

Solution for (2x-33)(4x-163)=180 equation:

(2x-33)(4x-163)=180

We move all terms to the left:

(2x-33)(4x-163)-(180)=0

We multiply parentheses ..

(+8x^2-326x-132x+5379)-180=0

We get rid of parentheses

8x^2-326x-132x+5379-180=0

We add all the numbers together, and all the variables

8x^2-458x+5199=0

a = 8; b = -458; c = +5199;
Δ = b2-4ac
Δ = -4582-4·8·5199
Δ = 43396
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:

$\sqrt{\Delta}=\sqrt{43396}=\sqrt{4*10849}=\sqrt{4}*\sqrt{10849}=2\sqrt{10849}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-458)-2\sqrt{10849}}{2*8}=\frac{458-2\sqrt{10849}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-458)+2\sqrt{10849}}{2*8}=\frac{458+2\sqrt{10849}}{16}
$