1/3a+1/6a=-1

Solution for 1/3a+1/6a=-1 equation:

1/3a+1/6a=-1

We move all terms to the left:

1/3a+1/6a-(-1)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 6a!=0

a!=0/6

a!=0

a∈R


We add all the numbers together, and all the variables

1/3a+1/6a+1=0

We calculate fractions


6a/18a^2+3a/18a^2+1=0

We multiply all the terms by the denominator


6a+3a+1*18a^2=0

We add all the numbers together, and all the variables

9a+1*18a^2=0

Wy multiply elements

18a^2+9a=0

a = 18; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·18·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*18}=\frac{-18}{36}
=-1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*18}=\frac{0}{36}
=0
$