3/4x=1/x-8

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

3/4x=1/x-8

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: x-8)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


3x+(-4x)+8*4x^2=0

Wy multiply elements

32x^2+3x+(-4x)=0

We get rid of parentheses

32x^2+3x-4x=0

We add all the numbers together, and all the variables

32x^2-1x=0

a = 32; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·32·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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