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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We multiply parentheses

3x*3)-(+24x-48+4=0

Wy multiply elements

9x^2+24x-48+4=0

We add all the numbers together, and all the variables

9x^2+24x-44=0

a = 9; b = 24; c = -44;
Δ = b2-4ac
Δ = 242-4·9·(-44)
Δ = 2160
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:

$\sqrt{\Delta}=\sqrt{2160}=\sqrt{144*15}=\sqrt{144}*\sqrt{15}=12\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12\sqrt{15}}{2*9}=\frac{-24-12\sqrt{15}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12\sqrt{15}}{2*9}=\frac{-24+12\sqrt{15}}{18}
$