6/7x-8=6/4x

Solution for 6/7x-8=6/4x equation:

6/7x-8=6/4x

We move all terms to the left:

6/7x-8-(6/4x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6/7x-(+6/4x)-8=0

We get rid of parentheses

6/7x-6/4x-8=0

We calculate fractions


24x/28x^2+(-42x)/28x^2-8=0

We multiply all the terms by the denominator


24x+(-42x)-8*28x^2=0

Wy multiply elements

-224x^2+24x+(-42x)=0

We get rid of parentheses

-224x^2+24x-42x=0

We add all the numbers together, and all the variables

-224x^2-18x=0

a = -224; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-224)·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*-224}=\frac{0}{-448}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-224}=\frac{36}{-448}
=-9/112
$