24n^2=-6n

Solution for 24n^2=-6n equation:

24n^2=-6n

We move all terms to the left:

24n^2-(-6n)=0

We get rid of parentheses

24n^2+6n=0

a = 24; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·24·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*24}=\frac{-12}{48}
=-1/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*24}=\frac{0}{48}
=0
$