12a^2+21a+9=0

Solution for 12a^2+21a+9=0 equation:

12a^2+21a+9=0

a = 12; b = 21; c = +9;
Δ = b2-4ac
Δ = 212-4·12·9
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3}{2*12}=\frac{-24}{24}
=-1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3}{2*12}=\frac{-18}{24}
=-3/4
$