1/x-3=1/4x

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

1/x-3=1/4x

We move all terms to the left:

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

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


4x+(-1x)-3*4x^2=0

Wy multiply elements

-12x^2+4x+(-1x)=0

We get rid of parentheses

-12x^2+4x-1x=0

We add all the numbers together, and all the variables

-12x^2+3x=0

a = -12; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-12)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-12}=\frac{-6}{-24}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-12}=\frac{0}{-24}
=0
$