1/2a-1/3a=4

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

1/2a-1/3a=4

We move all terms to the left:

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


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We calculate fractions


3a/6a^2+(-2a)/6a^2-4=0

We multiply all the terms by the denominator


3a+(-2a)-4*6a^2=0

Wy multiply elements

-24a^2+3a+(-2a)=0

We get rid of parentheses

-24a^2+3a-2a=0

We add all the numbers together, and all the variables

-24a^2+a=0

a = -24; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-24)·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*-24}=\frac{-2}{-48}
=1/24
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-24}=\frac{0}{-48}
=0
$