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

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



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

We move all terms to the left:

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



Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R





Domain of the equation: 3a-8)!=0

a∈R



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+11=0

We multiply all the terms by the denominator


3a+2a+11*6a^2=0

We add all the numbers together, and all the variables

5a+11*6a^2=0

Wy multiply elements

66a^2+5a=0

a = 66; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·66·0
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*66}=\frac{-10}{132}
=-5/66
$


$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*66}=\frac{0}{132}
=0
$

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