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9x^2+45x+54=0
a = 9; b = 45; c = +54;
Δ = b2-4ac
Δ = 452-4·9·54
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{81}=9$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-9}{2*9}=\frac{-54}{18} =-3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+9}{2*9}=\frac{-36}{18} =-2 $
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