(4x-2)(x-5)=28

Solution for (4x-2)(x-5)=28 equation:

(4x-2)(x-5)=28

We move all terms to the left:

(4x-2)(x-5)-(28)=0

We multiply parentheses ..

(+4x^2-20x-2x+10)-28=0

We get rid of parentheses

4x^2-20x-2x+10-28=0

We add all the numbers together, and all the variables

4x^2-22x-18=0

a = 4; b = -22; c = -18;
Δ = b2-4ac
Δ = -222-4·4·(-18)
Δ = 772
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:

$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{193}}{2*4}=\frac{22-2\sqrt{193}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{193}}{2*4}=\frac{22+2\sqrt{193}}{8}
$