20n-9/n=21

Solution for 20n-9/n=21 equation:

20n-9/n=21

We move all terms to the left:

20n-9/n-(21)=0


Domain of the equation: n!=0

n∈R


We multiply all the terms by the denominator


20n*n-21*n-9=0

We add all the numbers together, and all the variables

-21n+20n*n-9=0

Wy multiply elements

20n^2-21n-9=0

a = 20; b = -21; c = -9;
Δ = b2-4ac
Δ = -212-4·20·(-9)
Δ = 1161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1161}=\sqrt{9*129}=\sqrt{9}*\sqrt{129}=3\sqrt{129}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{129}}{2*20}=\frac{21-3\sqrt{129}}{40}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{129}}{2*20}=\frac{21+3\sqrt{129}}{40}
$