1/2x-16=5/8x

Solution for 1/2x-16=5/8x equation:

1/2x-16=5/8x

We move all terms to the left:

1/2x-16-(5/8x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(+5/8x)-16=0

We get rid of parentheses

1/2x-5/8x-16=0

We calculate fractions


8x/16x^2+(-10x)/16x^2-16=0

We multiply all the terms by the denominator


8x+(-10x)-16*16x^2=0

Wy multiply elements

-256x^2+8x+(-10x)=0

We get rid of parentheses

-256x^2+8x-10x=0

We add all the numbers together, and all the variables

-256x^2-2x=0

a = -256; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-256)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-256}=\frac{0}{-512}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-256}=\frac{4}{-512}
=-1/128
$