3/4x=6/3x+8

Solution for 3/4x=6/3x+8 equation:

3/4x=6/3x+8

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x+8)!=0

x∈R


We get rid of parentheses

3/4x-6/3x-8=0

We calculate fractions


9x/12x^2+(-24x)/12x^2-8=0

We multiply all the terms by the denominator


9x+(-24x)-8*12x^2=0

Wy multiply elements

-96x^2+9x+(-24x)=0

We get rid of parentheses

-96x^2+9x-24x=0

We add all the numbers together, and all the variables

-96x^2-15x=0

a = -96; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-96)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*-96}=\frac{0}{-192}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-96}=\frac{30}{-192}
=-5/32
$