1/4x-1/8x=-1/16

Solution for 1/4x-1/8x=-1/16 equation:

1/4x-1/8x=-1/16

We move all terms to the left:

1/4x-1/8x-(-1/16)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

1/4x-1/8x+1/16=0

We calculate fractions


256x^2/512x^2+128x/512x^2+(-64x)/512x^2=0

We multiply all the terms by the denominator


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

We get rid of parentheses

256x^2+128x-64x=0

We add all the numbers together, and all the variables

256x^2+64x=0

a = 256; b = 64; c = 0;
Δ = b2-4ac
Δ = 642-4·256·0
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*256}=\frac{-128}{512}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+64}{2*256}=\frac{0}{512}
=0
$