5/6x-3/4=3/8x

Solution for 5/6x-3/4=3/8x equation:

5/6x-3/4=3/8x

We move all terms to the left:

5/6x-3/4-(3/8x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/6x-(+3/8x)-3/4=0

We get rid of parentheses

5/6x-3/8x-3/4=0

We calculate fractions


(-1152x^2)/768x^2+640x/768x^2+(-288x)/768x^2=0

We multiply all the terms by the denominator


(-1152x^2)+640x+(-288x)=0

We get rid of parentheses

-1152x^2+640x-288x=0

We add all the numbers together, and all the variables

-1152x^2+352x=0

a = -1152; b = 352; c = 0;
Δ = b2-4ac
Δ = 3522-4·(-1152)·0
Δ = 123904
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{123904}=352$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(352)-352}{2*-1152}=\frac{-704}{-2304}
=11/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(352)+352}{2*-1152}=\frac{0}{-2304}
=0
$