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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x-1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


36x^2/48x^2+12x/48x^2+(-16x)/48x^2+1=0

We multiply all the terms by the denominator


36x^2+12x+(-16x)+1*48x^2=0

Wy multiply elements

36x^2+48x^2+12x+(-16x)=0

We get rid of parentheses

36x^2+48x^2+12x-16x=0

We add all the numbers together, and all the variables

84x^2-4x=0

a = 84; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·84·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*84}=\frac{0}{168}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*84}=\frac{8}{168}
=1/21
$