n/4+5=(51/2)n

Solution for n/4+5=(51/2)n equation:

n/4+5=(51/2)n

We move all terms to the left:

n/4+5-((51/2)n)=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

n/4-((+51/2)n)+5=0

We calculate fractions


2n^2/8n+()/8n+5=0

We multiply all the terms by the denominator


2n^2+5*8n+()=0

We add all the numbers together, and all the variables

2n^2+5*8n=0

Wy multiply elements

2n^2+40n=0

a = 2; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·2·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40}{2*2}=\frac{-80}{4}
=-20
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*2}=\frac{0}{4}
=0
$