/4n+5+n=20

Solution for /4n+5+n=20 equation:

/4n+5+n=20

We move all terms to the left:

/4n+5+n-(20)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We add all the numbers together, and all the variables

n+/4n-15=0

We multiply all the terms by the denominator


n*4n-15*4n+=0

We add all the numbers together, and all the variables

n*4n-15*4n=0

Wy multiply elements

4n^2-60n=0

a = 4; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·4·0
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{-(-60)-60}{2*4}=\frac{0}{8}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*4}=\frac{120}{8}
=15
$