n-5/n+8=27

Solution for n-5/n+8=27 equation:

n-5/n+8=27

We move all terms to the left:

n-5/n+8-(27)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

n-5/n-19=0

We multiply all the terms by the denominator


n*n-19*n-5=0

We add all the numbers together, and all the variables

-19n+n*n-5=0

Wy multiply elements

n^2-19n-5=0

a = 1; b = -19; c = -5;
Δ = b2-4ac
Δ = -192-4·1·(-5)
Δ = 381
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{-(-19)-\sqrt{381}}{2*1}=\frac{19-\sqrt{381}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{381}}{2*1}=\frac{19+\sqrt{381}}{2}
$