(-2/9)n+14=6

Solution for (-2/9)n+14=6 equation:

(-2/9)n+14=6

We move all terms to the left:

(-2/9)n+14-(6)=0


Domain of the equation: 9)n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(-2/9)n+8=0

We multiply parentheses

-2n^2+8=0

a = -2; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-2)·8
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*-2}=\frac{-8}{-4}
=+2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*-2}=\frac{8}{-4}
=-2
$