3/4n+1/2n=90

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

3/4n+1/2n=90

We move all terms to the left:

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


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We calculate fractions


6n/8n^2+4n/8n^2-90=0

We multiply all the terms by the denominator


6n+4n-90*8n^2=0

We add all the numbers together, and all the variables

10n-90*8n^2=0

Wy multiply elements

-720n^2+10n=0

a = -720; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-720)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-720}=\frac{-20}{-1440}
=1/72
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-720}=\frac{0}{-1440}
=0
$