x(3x-1)=x+5

Solution for x(3x-1)=x+5 equation:

x(3x-1)=x+5

We move all terms to the left:

x(3x-1)-(x+5)=0

We multiply parentheses

3x^2-1x-(x+5)=0

We get rid of parentheses

3x^2-1x-x-5=0

We add all the numbers together, and all the variables

3x^2-2x-5=0

a = 3; b = -2; c = -5;
Δ = b2-4ac
Δ = -22-4·3·(-5)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-8}{2*3}=\frac{-6}{6}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+8}{2*3}=\frac{10}{6}
=1+2/3
$