7a^2+24a+12=0

Solution for 7a^2+24a+12=0 equation:

7a^2+24a+12=0

a = 7; b = 24; c = +12;
Δ = b2-4ac
Δ = 242-4·7·12
Δ = 240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{15}}{2*7}=\frac{-24-4\sqrt{15}}{14}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{15}}{2*7}=\frac{-24+4\sqrt{15}}{14}
$