5/8x-6/7=4/3x

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Solution for 5/8x-6/7=4/3x equation: 



5/8x-6/7=4/3x

We move all terms to the left:

5/8x-6/7-(4/3x)=0



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R





Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R



We add all the numbers together, and all the variables

5/8x-(+4/3x)-6/7=0

We get rid of parentheses

5/8x-4/3x-6/7=0

We calculate fractions


(-432x^2)/1176x^2+735x/1176x^2+(-1568x)/1176x^2=0

We multiply all the terms by the denominator


(-432x^2)+735x+(-1568x)=0

We get rid of parentheses

-432x^2+735x-1568x=0

We add all the numbers together, and all the variables

-432x^2-833x=0

a = -432; b = -833; c = 0;
Δ = b2-4ac
Δ = -8332-4·(-432)·0
Δ = 693889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{693889}=833$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-833)-833}{2*-432}=\frac{0}{-864}
=0
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-833)+833}{2*-432}=\frac{1666}{-864}
=-1+401/432
$

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