2n-13/n=9/3

Solution for 2n-13/n=9/3 equation:

2n-13/n=9/3

We move all terms to the left:

2n-13/n-(9/3)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

2n-13/n-3=0

We multiply all the terms by the denominator


2n*n-3*n-13=0

We add all the numbers together, and all the variables

-3n+2n*n-13=0

Wy multiply elements

2n^2-3n-13=0

a = 2; b = -3; c = -13;
Δ = b2-4ac
Δ = -32-4·2·(-13)
Δ = 113
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{-(-3)-\sqrt{113}}{2*2}=\frac{3-\sqrt{113}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{113}}{2*2}=\frac{3+\sqrt{113}}{4}
$