3/4x+2=8/3x-4

Solution for 3/4x+2=8/3x-4 equation:

3/4x+2=8/3x-4

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

3/4x-8/3x+4+2=0

We calculate fractions


9x/12x^2+(-32x)/12x^2+4+2=0

We add all the numbers together, and all the variables

9x/12x^2+(-32x)/12x^2+6=0

We multiply all the terms by the denominator


9x+(-32x)+6*12x^2=0

Wy multiply elements

72x^2+9x+(-32x)=0

We get rid of parentheses

72x^2+9x-32x=0

We add all the numbers together, and all the variables

72x^2-23x=0

a = 72; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·72·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*72}=\frac{0}{144}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*72}=\frac{46}{144}
=23/72
$