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2a^2+24a+54=0
a = 2; b = 24; c = +54;
Δ = b2-4ac
Δ = 242-4·2·54
Δ = 144
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{144}=12$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12}{2*2}=\frac{-36}{4} =-9 $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12}{2*2}=\frac{-12}{4} =-3 $
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