(3/4)n+(1/2)n=90

Solution for (3/4)n+(1/2)n=90 equation:

(3/4)n+(1/2)n=90

We move all terms to the left:

(3/4)n+(1/2)n-(90)=0


Domain of the equation: 4)n!=0

n!=0/1

n!=0

n∈R



Domain of the equation: 2)n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(+3/4)n+(+1/2)n-90=0

We multiply parentheses

3n^2+n^2-90=0

We add all the numbers together, and all the variables

4n^2-90=0

a = 4; b = 0; c = -90;
Δ = b2-4ac
Δ = 02-4·4·(-90)
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{10}}{2*4}=\frac{0-12\sqrt{10}}{8}
=-\frac{12\sqrt{10}}{8}
=-\frac{3\sqrt{10}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{10}}{2*4}=\frac{0+12\sqrt{10}}{8}
=\frac{12\sqrt{10}}{8}
=\frac{3\sqrt{10}}{2}
$