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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-512x)/1024x^2+(-10x)/1024x^2+6x/1024x^2-1=0

We multiply all the terms by the denominator


(-512x)+(-10x)+6x-1*1024x^2=0

We add all the numbers together, and all the variables

6x+(-512x)+(-10x)-1*1024x^2=0

Wy multiply elements

-1024x^2+6x+(-512x)+(-10x)=0

We get rid of parentheses

-1024x^2+6x-512x-10x=0

We add all the numbers together, and all the variables

-1024x^2-516x=0

a = -1024; b = -516; c = 0;
Δ = b2-4ac
Δ = -5162-4·(-1024)·0
Δ = 266256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{266256}=516$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-516)-516}{2*-1024}=\frac{0}{-2048}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-516)+516}{2*-1024}=\frac{1032}{-2048}
=-129/256
$