3x(x-2)=x+8

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

3x(x-2)=x+8

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2-7x-8=0

a = 3; b = -7; c = -8;
Δ = b2-4ac
Δ = -72-4·3·(-8)
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{145}}{2*3}=\frac{7-\sqrt{145}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{145}}{2*3}=\frac{7+\sqrt{145}}{6}
$