5/6x-3/8x=7/12

Solution for 5/6x-3/8x=7/12 equation:

5/6x-3/8x=7/12

We move all terms to the left:

5/6x-3/8x-(7/12)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

5/6x-3/8x-(+7/12)=0

We get rid of parentheses

5/6x-3/8x-7/12=0

We calculate fractions


(-2688x^2)/576x^2+480x/576x^2+(-216x)/576x^2=0

We multiply all the terms by the denominator


(-2688x^2)+480x+(-216x)=0

We get rid of parentheses

-2688x^2+480x-216x=0

We add all the numbers together, and all the variables

-2688x^2+264x=0

a = -2688; b = 264; c = 0;
Δ = b2-4ac
Δ = 2642-4·(-2688)·0
Δ = 69696
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{69696}=264$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(264)-264}{2*-2688}=\frac{-528}{-5376}
=11/112
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(264)+264}{2*-2688}=\frac{0}{-5376}
=0
$