21n^2=2-11n

Solution for 21n^2=2-11n equation:

21n^2=2-11n

We move all terms to the left:

21n^2-(2-11n)=0

We add all the numbers together, and all the variables

21n^2-(-11n+2)=0

We get rid of parentheses

21n^2+11n-2=0

a = 21; b = 11; c = -2;
Δ = b2-4ac
Δ = 112-4·21·(-2)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-17}{2*21}=\frac{-28}{42}
=-2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+17}{2*21}=\frac{6}{42}
=1/7
$