(5/2)n=180

Solution for (5/2)n=180 equation:

(5/2)n=180

We move all terms to the left:

(5/2)n-(180)=0


Domain of the equation: 2)n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(+5/2)n-180=0

We multiply parentheses

5n^2-180=0

a = 5; b = 0; c = -180;
Δ = b2-4ac
Δ = 02-4·5·(-180)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60}{2*5}=\frac{-60}{10}
=-6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60}{2*5}=\frac{60}{10}
=6
$