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

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

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

We move all terms to the left:

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

We multiply parentheses

4x^2-12x-(8x+2)=0

We get rid of parentheses

4x^2-12x-8x-2=0

We add all the numbers together, and all the variables

4x^2-20x-2=0

a = 4; b = -20; c = -2;
Δ = b2-4ac
Δ = -202-4·4·(-2)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-12\sqrt{3}}{2*4}=\frac{20-12\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+12\sqrt{3}}{2*4}=\frac{20+12\sqrt{3}}{8}
$