3x(x+2)-2x(x+6)=8

Solution for 3x(x+2)-2x(x+6)=8 equation:

3x(x+2)-2x(x+6)=8

We move all terms to the left:

3x(x+2)-2x(x+6)-(8)=0

We multiply parentheses

3x^2-2x^2+6x-12x-8=0

We add all the numbers together, and all the variables

x^2-6x-8=0

a = 1; b = -6; c = -8;
Δ = b2-4ac
Δ = -62-4·1·(-8)
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{17}}{2*1}=\frac{6-2\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{17}}{2*1}=\frac{6+2\sqrt{17}}{2}
$