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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We multiply parentheses

3x*3)-(+16x-24+3=0

Wy multiply elements

9x^2+16x-24+3=0

We add all the numbers together, and all the variables

9x^2+16x-21=0

a = 9; b = 16; c = -21;
Δ = b2-4ac
Δ = 162-4·9·(-21)
Δ = 1012
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:

$\sqrt{\Delta}=\sqrt{1012}=\sqrt{4*253}=\sqrt{4}*\sqrt{253}=2\sqrt{253}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{253}}{2*9}=\frac{-16-2\sqrt{253}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{253}}{2*9}=\frac{-16+2\sqrt{253}}{18}
$