1/3a-a-6=15

Solution for 1/3a-a-6=15 equation:

1/3a-a-6=15

We move all terms to the left:

1/3a-a-6-(15)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We add all the numbers together, and all the variables

-1a+1/3a-21=0

We multiply all the terms by the denominator


-1a*3a-21*3a+1=0

Wy multiply elements

-3a^2-63a+1=0

a = -3; b = -63; c = +1;
Δ = b2-4ac
Δ = -632-4·(-3)·1
Δ = 3981
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-\sqrt{3981}}{2*-3}=\frac{63-\sqrt{3981}}{-6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+\sqrt{3981}}{2*-3}=\frac{63+\sqrt{3981}}{-6}
$