-6/7+1/4x=5/2x

Solution for -6/7+1/4x=5/2x equation:

-6/7+1/4x=5/2x

We move all terms to the left:

-6/7+1/4x-(5/2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x-(+5/2x)-6/7=0

We get rid of parentheses

1/4x-5/2x-6/7=0

We calculate fractions


(-96x^2)/392x^2+98x/392x^2+(-980x)/392x^2=0

We multiply all the terms by the denominator


(-96x^2)+98x+(-980x)=0

We get rid of parentheses

-96x^2+98x-980x=0

We add all the numbers together, and all the variables

-96x^2-882x=0

a = -96; b = -882; c = 0;
Δ = b2-4ac
Δ = -8822-4·(-96)·0
Δ = 777924
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{777924}=882$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-882)-882}{2*-96}=\frac{0}{-192}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-882)+882}{2*-96}=\frac{1764}{-192}
=-9+3/16
$