2n-5/n=9

Solution for 2n-5/n=9 equation:

2n-5/n=9

We move all terms to the left:

2n-5/n-(9)=0


Domain of the equation: n!=0

n∈R


We multiply all the terms by the denominator


2n*n-9*n-5=0

We add all the numbers together, and all the variables

-9n+2n*n-5=0

Wy multiply elements

2n^2-9n-5=0

a = 2; b = -9; c = -5;
Δ = b2-4ac
Δ = -92-4·2·(-5)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-11}{2*2}=\frac{-2}{4}
=-1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+11}{2*2}=\frac{20}{4}
=5
$