5/6x-7=7/8x

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

5/6x-7=7/8x

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


40x/48x^2+(-42x)/48x^2-7=0

We multiply all the terms by the denominator


40x+(-42x)-7*48x^2=0

Wy multiply elements

-336x^2+40x+(-42x)=0

We get rid of parentheses

-336x^2+40x-42x=0

We add all the numbers together, and all the variables

-336x^2-2x=0

a = -336; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-336)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-336}=\frac{0}{-672}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-336}=\frac{4}{-672}
=-1/168
$