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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

3x^2-2x-24x-(x+6)=0

We get rid of parentheses

3x^2-2x-24x-x-6=0

We add all the numbers together, and all the variables

3x^2-27x-6=0

a = 3; b = -27; c = -6;
Δ = b2-4ac
Δ = -272-4·3·(-6)
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{89}}{2*3}=\frac{27-3\sqrt{89}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{89}}{2*3}=\frac{27+3\sqrt{89}}{6}
$