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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


12x^2/96x^2+(-32x)/96x^2+(-48x)/96x^2=0

We multiply all the terms by the denominator


12x^2+(-32x)+(-48x)=0

We get rid of parentheses

12x^2-32x-48x=0

We add all the numbers together, and all the variables

12x^2-80x=0

a = 12; b = -80; c = 0;
Δ = b2-4ac
Δ = -802-4·12·0
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-80}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+80}{2*12}=\frac{160}{24}
=6+2/3
$