3a(8a+3)=0

Solution for 3a(8a+3)=0 equation:

3a(8a+3)=0

We multiply parentheses

24a^2+9a=0

a = 24; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·24·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*24}=\frac{-18}{48}
=-3/8
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*24}=\frac{0}{48}
=0
$