6x(x-2)-x=5

Solution for 6x(x-2)-x=5 equation:

6x(x-2)-x=5

We move all terms to the left:

6x(x-2)-x-(5)=0

We add all the numbers together, and all the variables

-1x+6x(x-2)-5=0

We multiply parentheses

6x^2-1x-12x-5=0

We add all the numbers together, and all the variables

6x^2-13x-5=0

a = 6; b = -13; c = -5;
Δ = b2-4ac
Δ = -132-4·6·(-5)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-17}{2*6}=\frac{-4}{12}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+17}{2*6}=\frac{30}{12}
=2+1/2
$