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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x+4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


8x/12x^2+(-6x)/12x^2-4-3=0

We add all the numbers together, and all the variables

8x/12x^2+(-6x)/12x^2-7=0

We multiply all the terms by the denominator


8x+(-6x)-7*12x^2=0

Wy multiply elements

-84x^2+8x+(-6x)=0

We get rid of parentheses

-84x^2+8x-6x=0

We add all the numbers together, and all the variables

-84x^2+2x=0

a = -84; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-84)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-84}=\frac{-4}{-168}
=1/42
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-84}=\frac{0}{-168}
=0
$