(4x-28)(x-2)=180

Solution for (4x-28)(x-2)=180 equation:

(4x-28)(x-2)=180

We move all terms to the left:

(4x-28)(x-2)-(180)=0

We multiply parentheses ..

(+4x^2-8x-28x+56)-180=0

We get rid of parentheses

4x^2-8x-28x+56-180=0

We add all the numbers together, and all the variables

4x^2-36x-124=0

a = 4; b = -36; c = -124;
Δ = b2-4ac
Δ = -362-4·4·(-124)
Δ = 3280
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:

$\sqrt{\Delta}=\sqrt{3280}=\sqrt{16*205}=\sqrt{16}*\sqrt{205}=4\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{205}}{2*4}=\frac{36-4\sqrt{205}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{205}}{2*4}=\frac{36+4\sqrt{205}}{8}
$