8/3x-5/8=3/2x

Solution for 8/3x-5/8=3/2x equation:

8/3x-5/8=3/2x

We move all terms to the left:

8/3x-5/8-(3/2x)=0


Domain of the equation: 3x!=0

x!=0/3

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

8/3x-(+3/2x)-5/8=0

We get rid of parentheses

8/3x-3/2x-5/8=0

We calculate fractions


(-60x^2)/384x^2+1024x/384x^2+(-576x)/384x^2=0

We multiply all the terms by the denominator


(-60x^2)+1024x+(-576x)=0

We get rid of parentheses

-60x^2+1024x-576x=0

We add all the numbers together, and all the variables

-60x^2+448x=0

a = -60; b = 448; c = 0;
Δ = b2-4ac
Δ = 4482-4·(-60)·0
Δ = 200704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{200704}=448$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(448)-448}{2*-60}=\frac{-896}{-120}
=7+7/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(448)+448}{2*-60}=\frac{0}{-120}
=0
$