x(x+21)=0

Solution for x(x+21)=0 equation:

x(x+21)=0

We multiply parentheses

x^2+21x=0

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

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