3/4x=1/x-2

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

3/4x=1/x-2

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: x-2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

8x^2+3x-4x=0

We add all the numbers together, and all the variables

8x^2-1x=0

a = 8; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·8·0
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*8}=\frac{0}{16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*8}=\frac{2}{16}
=1/8
$