5/12-3/4x=7/6x

Solution for 5/12-3/4x=7/6x equation:

5/12-3/4x=7/6x

We move all terms to the left:

5/12-3/4x-(7/6x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-3/4x-(+7/6x)+5/12=0

We get rid of parentheses

-3/4x-7/6x+5/12=0

We calculate fractions


720x^2/288x^2+(-216x)/288x^2+(-336x)/288x^2=0

We multiply all the terms by the denominator


720x^2+(-216x)+(-336x)=0

We get rid of parentheses

720x^2-216x-336x=0

We add all the numbers together, and all the variables

720x^2-552x=0

a = 720; b = -552; c = 0;
Δ = b2-4ac
Δ = -5522-4·720·0
Δ = 304704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{304704}=552$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-552)-552}{2*720}=\frac{0}{1440}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-552)+552}{2*720}=\frac{1104}{1440}
=23/30
$