(22/33)n-3=8

Solution for (22/33)n-3=8 equation:

(22/33)n-3=8

We move all terms to the left:

(22/33)n-3-(8)=0


Domain of the equation: 33)n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(+22/33)n-3-8=0

We add all the numbers together, and all the variables

(+22/33)n-11=0

We multiply parentheses

22n^2-11=0

a = 22; b = 0; c = -11;
Δ = b2-4ac
Δ = 02-4·22·(-11)
Δ = 968
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{968}=\sqrt{484*2}=\sqrt{484}*\sqrt{2}=22\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-22\sqrt{2}}{2*22}=\frac{0-22\sqrt{2}}{44}
=-\frac{22\sqrt{2}}{44}
=-\frac{\sqrt{2}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+22\sqrt{2}}{2*22}=\frac{0+22\sqrt{2}}{44}
=\frac{22\sqrt{2}}{44}
=\frac{\sqrt{2}}{2}
$