(11/4)n=36

Solution for (11/4)n=36 equation:

(11/4)n=36

We move all terms to the left:

(11/4)n-(36)=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

(+11/4)n-36=0

We multiply parentheses

11n^2-36=0

a = 11; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·11·(-36)
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{11}}{2*11}=\frac{0-12\sqrt{11}}{22}
=-\frac{12\sqrt{11}}{22}
=-\frac{6\sqrt{11}}{11}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{11}}{2*11}=\frac{0+12\sqrt{11}}{22}
=\frac{12\sqrt{11}}{22}
=\frac{6\sqrt{11}}{11}
$