n-13=24/n=11

Solution for n-13=24/n=11 equation:

n-13=24/n=11

We move all terms to the left:

n-13-(24/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-(+24/n)-13=0

We get rid of parentheses

n-24/n-13=0

We multiply all the terms by the denominator


n*n-13*n-24=0

We add all the numbers together, and all the variables

-13n+n*n-24=0

Wy multiply elements

n^2-13n-24=0

a = 1; b = -13; c = -24;
Δ = b2-4ac
Δ = -132-4·1·(-24)
Δ = 265
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{265}}{2*1}=\frac{13-\sqrt{265}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{265}}{2*1}=\frac{13+\sqrt{265}}{2}
$