C(n)=-6(-1/3)n-1

Solution for C(n)=-6(-1/3)n-1 equation:

(C)=-6(-1/3)C-1

We move all terms to the left:

(C)-(-6(-1/3)C-1)=0


Domain of the equation: 3)C-1)!=0

C!=0/1

C!=0

C∈R


We multiply all the terms by the denominator


C*3)C-1)-(-6(-1=0

Wy multiply elements

3C^2-1=0

a = 3; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·3·(-1)
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{3}}{2*3}=\frac{0-2\sqrt{3}}{6}
=-\frac{2\sqrt{3}}{6}
=-\frac{\sqrt{3}}{3}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{3}}{2*3}=\frac{0+2\sqrt{3}}{6}
=\frac{2\sqrt{3}}{6}
=\frac{\sqrt{3}}{3}
$