2/x-3/8x=1/4

Solution for 2/x-3/8x=1/4 equation:

2/x-3/8x=1/4

We move all terms to the left:

2/x-3/8x-(1/4)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2/x-3/8x-1/4=0

We calculate fractions


(-64x^2)/128x^2+256x/128x^2+(-48x)/128x^2=0

We multiply all the terms by the denominator


(-64x^2)+256x+(-48x)=0

We get rid of parentheses

-64x^2+256x-48x=0

We add all the numbers together, and all the variables

-64x^2+208x=0

a = -64; b = 208; c = 0;
Δ = b2-4ac
Δ = 2082-4·(-64)·0
Δ = 43264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{43264}=208$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(208)-208}{2*-64}=\frac{-416}{-128}
=3+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(208)+208}{2*-64}=\frac{0}{-128}
=0
$