4/3x-1=12-4x

Solution for 4/3x-1=12-4x equation:

4/3x-1=12-4x

We move all terms to the left:

4/3x-1-(12-4x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

4/3x-(-4x+12)-1=0

We get rid of parentheses

4/3x+4x-12-1=0

We multiply all the terms by the denominator


4x*3x-12*3x-1*3x+4=0

Wy multiply elements

12x^2-36x-3x+4=0

We add all the numbers together, and all the variables

12x^2-39x+4=0

a = 12; b = -39; c = +4;
Δ = b2-4ac
Δ = -392-4·12·4
Δ = 1329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-\sqrt{1329}}{2*12}=\frac{39-\sqrt{1329}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{1329}}{2*12}=\frac{39+\sqrt{1329}}{24}
$