n-16+4/5n=24

Solution for n-16+4/5n=24 equation:

n-16+4/5n=24

We move all terms to the left:

n-16+4/5n-(24)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We add all the numbers together, and all the variables

n+4/5n-40=0

We multiply all the terms by the denominator


n*5n-40*5n+4=0

Wy multiply elements

5n^2-200n+4=0

a = 5; b = -200; c = +4;
Δ = b2-4ac
Δ = -2002-4·5·4
Δ = 39920
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:

$\sqrt{\Delta}=\sqrt{39920}=\sqrt{16*2495}=\sqrt{16}*\sqrt{2495}=4\sqrt{2495}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-4\sqrt{2495}}{2*5}=\frac{200-4\sqrt{2495}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+4\sqrt{2495}}{2*5}=\frac{200+4\sqrt{2495}}{10}
$