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18a^2-43a+24=0
a = 18; b = -43; c = +24;
Δ = b2-4ac
Δ = -432-4·18·24
Δ = 121
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{121}=11$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-11}{2*18}=\frac{32}{36} =8/9 $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+11}{2*18}=\frac{54}{36} =1+1/2 $
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