23+n=50/n=73

Solution for 23+n=50/n=73 equation:

23+n=50/n=73

We move all terms to the left:

23+n-(50/n)=0


Domain of the equation: n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

n-(+50/n)+23=0

We get rid of parentheses

n-50/n+23=0

We multiply all the terms by the denominator


n*n+23*n-50=0

We add all the numbers together, and all the variables

23n+n*n-50=0

Wy multiply elements

n^2+23n-50=0

a = 1; b = 23; c = -50;
Δ = b2-4ac
Δ = 232-4·1·(-50)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-27}{2*1}=\frac{-50}{2}
=-25
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+27}{2*1}=\frac{4}{2}
=2
$