1/3a-1/2a=1/2+2

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

1/3a-1/2a=1/2+2

We move all terms to the left:

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


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We get rid of parentheses

1/3a-1/2a-2-1/2=0

We calculate fractions


8a/24a^2+(-3a)/24a^2+(-3a)/24a^2-2=0

We multiply all the terms by the denominator


8a+(-3a)+(-3a)-2*24a^2=0

Wy multiply elements

-48a^2+8a+(-3a)+(-3a)=0

We get rid of parentheses

-48a^2+8a-3a-3a=0

We add all the numbers together, and all the variables

-48a^2+2a=0

a = -48; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-48)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-48}=\frac{-4}{-96}
=1/24
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-48}=\frac{0}{-96}
=0
$