3/x+1/8=13/4x

Solution for 3/x+1/8=13/4x equation:

3/x+1/8=13/4x

We move all terms to the left:

3/x+1/8-(13/4x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/x-(+13/4x)+1/8=0

We get rid of parentheses

3/x-13/4x+1/8=0

We calculate fractions


16x^2/256x^2+768x/256x^2+(-832x)/256x^2=0

We multiply all the terms by the denominator


16x^2+768x+(-832x)=0

We get rid of parentheses

16x^2+768x-832x=0

We add all the numbers together, and all the variables

16x^2-64x=0

a = 16; b = -64; c = 0;
Δ = b2-4ac
Δ = -642-4·16·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-64}{2*16}=\frac{0}{32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+64}{2*16}=\frac{128}{32}
=4
$