21n^2=-12n

Solution for 21n^2=-12n equation:

21n^2=-12n

We move all terms to the left:

21n^2-(-12n)=0

We get rid of parentheses

21n^2+12n=0

a = 21; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·21·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*21}=\frac{-24}{42}
=-4/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*21}=\frac{0}{42}
=0
$