-1/2x+2/3=5/8x-3

Solution for -1/2x+2/3=5/8x-3 equation:

-1/2x+2/3=5/8x-3

We move all terms to the left:

-1/2x+2/3-(5/8x-3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x-3)!=0

x∈R


We get rid of parentheses

-1/2x-5/8x+3+2/3=0

We calculate fractions


256x^2/144x^2+(-72x)/144x^2+(-90x)/144x^2+3=0

We multiply all the terms by the denominator


256x^2+(-72x)+(-90x)+3*144x^2=0

Wy multiply elements

256x^2+432x^2+(-72x)+(-90x)=0

We get rid of parentheses

256x^2+432x^2-72x-90x=0

We add all the numbers together, and all the variables

688x^2-162x=0

a = 688; b = -162; c = 0;
Δ = b2-4ac
Δ = -1622-4·688·0
Δ = 26244
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{26244}=162$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-162)-162}{2*688}=\frac{0}{1376}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-162)+162}{2*688}=\frac{324}{1376}
=81/344
$