3a(a+7)=0

Solution for 3a(a+7)=0 equation:

3a(a+7)=0

We multiply parentheses

3a^2+21a=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:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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