2x(x-4)=6x+8

Solution for 2x(x-4)=6x+8 equation:

2x(x-4)=6x+8

We move all terms to the left:

2x(x-4)-(6x+8)=0

We multiply parentheses

2x^2-8x-(6x+8)=0

We get rid of parentheses

2x^2-8x-6x-8=0

We add all the numbers together, and all the variables

2x^2-14x-8=0

a = 2; b = -14; c = -8;
Δ = b2-4ac
Δ = -142-4·2·(-8)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{65}}{2*2}=\frac{14-2\sqrt{65}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{65}}{2*2}=\frac{14+2\sqrt{65}}{4}
$