21n(-1+10/21n+1)=10

Solution for 21n(-1+10/21n+1)=10 equation:

21n(-1+10/21n+1)=10

We move all terms to the left:

21n(-1+10/21n+1)-(10)=0


Domain of the equation: 21n+1)!=0

n∈R


We add all the numbers together, and all the variables

21n(+10/21n)-10=0

We multiply parentheses

210n^2-10=0

a = 210; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·210·(-10)
Δ = 8400
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:

$\sqrt{\Delta}=\sqrt{8400}=\sqrt{400*21}=\sqrt{400}*\sqrt{21}=20\sqrt{21}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{21}}{2*210}=\frac{0-20\sqrt{21}}{420}
=-\frac{20\sqrt{21}}{420}
=-\frac{\sqrt{21}}{21}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{21}}{2*210}=\frac{0+20\sqrt{21}}{420}
=\frac{20\sqrt{21}}{420}
=\frac{\sqrt{21}}{21}
$