1/3a-1=1/4a

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

1/3a-1=1/4a

We move all terms to the left:

1/3a-1-(1/4a)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 4a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/3a-1/4a-1=0

We calculate fractions


4a/12a^2+(-3a)/12a^2-1=0

We multiply all the terms by the denominator


4a+(-3a)-1*12a^2=0

Wy multiply elements

-12a^2+4a+(-3a)=0

We get rid of parentheses

-12a^2+4a-3a=0

We add all the numbers together, and all the variables

-12a^2+a=0

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

$\sqrt{\Delta}=\sqrt{1}=1$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-12}=\frac{-2}{-24}
=1/12
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-12}=\frac{0}{-24}
=0
$