2a^2+18a+24=0

Solution for 2a^2+18a+24=0 equation:

2a^2+18a+24=0

a = 2; b = 18; c = +24;
Δ = b2-4ac
Δ = 182-4·2·24
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{33}}{2*2}=\frac{-18-2\sqrt{33}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{33}}{2*2}=\frac{-18+2\sqrt{33}}{4}
$