6(3x-8)=x(6-4)

Solution for 6(3x-8)=x(6-4) equation:

6(3x-8)=x(6-4)

We move all terms to the left:

6(3x-8)-(x(6-4))=0

We add all the numbers together, and all the variables

6(3x-8)-(x2)=0

We add all the numbers together, and all the variables

-1x^2+6(3x-8)=0

We multiply parentheses

-1x^2+18x-48=0

a = -1; b = 18; c = -48;
Δ = b2-4ac
Δ = 182-4·(-1)·(-48)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{33}}{2*-1}=\frac{-18-2\sqrt{33}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{33}}{2*-1}=\frac{-18+2\sqrt{33}}{-2}
$