3x-4/2=42-4/3x

Solution for 3x-4/2=42-4/3x equation:

3x-4/2=42-4/3x

We move all terms to the left:

3x-4/2-(42-4/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(-4/3x+42)-4/2=0

We add all the numbers together, and all the variables

3x-(-4/3x+42)-2=0

We get rid of parentheses

3x+4/3x-42-2=0

We multiply all the terms by the denominator


3x*3x-42*3x-2*3x+4=0

Wy multiply elements

9x^2-126x-6x+4=0

We add all the numbers together, and all the variables

9x^2-132x+4=0

a = 9; b = -132; c = +4;
Δ = b2-4ac
Δ = -1322-4·9·4
Δ = 17280
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:

$\sqrt{\Delta}=\sqrt{17280}=\sqrt{576*30}=\sqrt{576}*\sqrt{30}=24\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-24\sqrt{30}}{2*9}=\frac{132-24\sqrt{30}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+24\sqrt{30}}{2*9}=\frac{132+24\sqrt{30}}{18}
$