(3/4)n-14=-8

Solution for (3/4)n-14=-8 equation:

(3/4)n-14=-8

We move all terms to the left:

(3/4)n-14-(-8)=0


Domain of the equation: 4)n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(+3/4)n-14-(-8)=0

We add all the numbers together, and all the variables

(+3/4)n-6=0

We multiply parentheses

3n^2-6=0

a = 3; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·3·(-6)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{2}}{2*3}=\frac{0-6\sqrt{2}}{6}
=-\frac{6\sqrt{2}}{6}
=-\sqrt{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{2}}{2*3}=\frac{0+6\sqrt{2}}{6}
=\frac{6\sqrt{2}}{6}
=\sqrt{2}
$