-2/3x+6=4x-8

Solution for -2/3x+6=4x-8 equation:

-2/3x+6=4x-8

We move all terms to the left:

-2/3x+6-(4x-8)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

-2/3x-4x+8+6=0

We multiply all the terms by the denominator


-4x*3x+8*3x+6*3x-2=0

Wy multiply elements

-12x^2+24x+18x-2=0

We add all the numbers together, and all the variables

-12x^2+42x-2=0

a = -12; b = 42; c = -2;
Δ = b2-4ac
Δ = 422-4·(-12)·(-2)
Δ = 1668
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:

$\sqrt{\Delta}=\sqrt{1668}=\sqrt{4*417}=\sqrt{4}*\sqrt{417}=2\sqrt{417}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{417}}{2*-12}=\frac{-42-2\sqrt{417}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{417}}{2*-12}=\frac{-42+2\sqrt{417}}{-24}
$