1/x+1/2x=1/4

Solution for 1/x+1/2x=1/4 equation:

1/x+1/2x=1/4

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-4x^2)/32x^2+32x/32x^2+16x/32x^2=0

We multiply all the terms by the denominator


(-4x^2)+32x+16x=0

We add all the numbers together, and all the variables

(-4x^2)+48x=0

We get rid of parentheses

-4x^2+48x=0

a = -4; b = 48; c = 0;
Δ = b2-4ac
Δ = 482-4·(-4)·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-48}{2*-4}=\frac{-96}{-8}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+48}{2*-4}=\frac{0}{-8}
=0
$