-3u(u+7)=0

Solution for -3u(u+7)=0 equation:

-3u(u+7)=0

We multiply parentheses

-3u^2-21u=0

a = -3; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·(-3)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*-3}=\frac{0}{-6}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*-3}=\frac{42}{-6}
=-7
$