7n^2=-2n

Solution for 7n^2=-2n equation:

7n^2=-2n

We move all terms to the left:

7n^2-(-2n)=0

We get rid of parentheses

7n^2+2n=0

a = 7; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·7·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*7}=\frac{-4}{14}
=-2/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*7}=\frac{0}{14}
=0
$