6n^2=-16n

Solution for 6n^2=-16n equation:

6n^2=-16n

We move all terms to the left:

6n^2-(-16n)=0

We get rid of parentheses

6n^2+16n=0

a = 6; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·6·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*6}=\frac{-32}{12}
=-2+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*6}=\frac{0}{12}
=0
$