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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x-1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

Fractions to decimals

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

96x^2+4x=0

a = 96; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·96·0
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*96}=\frac{-8}{192}
=-1/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*96}=\frac{0}{192}
=0
$