9=-3/n+2n

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

9=-3/n+2n

We move all terms to the left:

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


Domain of the equation: n+2n)!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-2n+3/n+9=0

We multiply all the terms by the denominator


-2n*n+9*n+3=0

We add all the numbers together, and all the variables

9n-2n*n+3=0

Wy multiply elements

-2n^2+9n+3=0

a = -2; b = 9; c = +3;
Δ = b2-4ac
Δ = 92-4·(-2)·3
Δ = 105
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{-(9)-\sqrt{105}}{2*-2}=\frac{-9-\sqrt{105}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{105}}{2*-2}=\frac{-9+\sqrt{105}}{-4}
$