6u^2=-24u

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

6u^2=-24u

We move all terms to the left:

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

We get rid of parentheses

6u^2+24u=0

a = 6; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·6·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*6}=\frac{-48}{12}
=-4
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*6}=\frac{0}{12}
=0
$