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X^2-27X+30=0
a = 1; b = -27; c = +30;
Δ = b2-4ac
Δ = -272-4·1·30
Δ = 609
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-\sqrt{609}}{2*1}=\frac{27-\sqrt{609}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{609}}{2*1}=\frac{27+\sqrt{609}}{2} $
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