X/6=3x/4x

Solution for X/6=3x/4x equation:

X/6=3X/4X

We move all terms to the left:

X/6-(3X/4X)=0


Domain of the equation: 4X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X/6-(+3X/4X)=0

We get rid of parentheses

X/6-3X/4X=0

We calculate fractions


4X^2/24X+(-18X)/24X=0

We multiply all the terms by the denominator


4X^2+(-18X)=0

We get rid of parentheses

4X^2-18X=0

a = 4; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·4·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*4}=\frac{0}{8}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*4}=\frac{36}{8}
=4+1/2
$