4/3x+2=4x-4

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

4/3x+2=4x-4

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-12x^2+12x+6x+4=0

We add all the numbers together, and all the variables

-12x^2+18x+4=0

a = -12; b = 18; c = +4;
Δ = b2-4ac
Δ = 182-4·(-12)·4
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{129}}{2*-12}=\frac{-18-2\sqrt{129}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{129}}{2*-12}=\frac{-18+2\sqrt{129}}{-24}
$