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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We add all the numbers together, and all the variables

2x^2-15x-8=0

a = 2; b = -15; c = -8;
Δ = b2-4ac
Δ = -152-4·2·(-8)
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{-(-15)-17}{2*2}=\frac{-2}{4}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+17}{2*2}=\frac{32}{4}
=8
$