1/2a+3=8-1/3a

Solution for 1/2a+3=8-1/3a equation:

1/2a+3=8-1/3a

We move all terms to the left:

1/2a+3-(8-1/3a)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 3a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

1/2a-(-1/3a+8)+3=0

We get rid of parentheses

1/2a+1/3a-8+3=0

We calculate fractions


3a/6a^2+2a/6a^2-8+3=0

We add all the numbers together, and all the variables

3a/6a^2+2a/6a^2-5=0

We multiply all the terms by the denominator


3a+2a-5*6a^2=0

We add all the numbers together, and all the variables

5a-5*6a^2=0

Wy multiply elements

-30a^2+5a=0

a = -30; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-30)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-30}=\frac{-10}{-60}
=1/6
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-30}=\frac{0}{-60}
=0
$