(-2+3x)(-8+2x)=4

Solution for (-2+3x)(-8+2x)=4 equation:

(-2+3x)(-8+2x)=4

We move all terms to the left:

(-2+3x)(-8+2x)-(4)=0

We add all the numbers together, and all the variables

(3x-2)(2x-8)-4=0

We multiply parentheses ..

(+6x^2-24x-4x+16)-4=0

We get rid of parentheses

6x^2-24x-4x+16-4=0

We add all the numbers together, and all the variables

6x^2-28x+12=0

a = 6; b = -28; c = +12;
Δ = b2-4ac
Δ = -282-4·6·12
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{31}}{2*6}=\frac{28-4\sqrt{31}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{31}}{2*6}=\frac{28+4\sqrt{31}}{12}
$