5n-9/n+6=2

Solution for 5n-9/n+6=2 equation:

5n-9/n+6=2

We move all terms to the left:

5n-9/n+6-(2)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

5n-9/n+4=0

We multiply all the terms by the denominator


5n*n+4*n-9=0

We add all the numbers together, and all the variables

4n+5n*n-9=0

Wy multiply elements

5n^2+4n-9=0

a = 5; b = 4; c = -9;
Δ = b2-4ac
Δ = 42-4·5·(-9)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-14}{2*5}=\frac{-18}{10}
=-1+4/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+14}{2*5}=\frac{10}{10}
=1
$