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165+27x+x^2=0
a = 1; b = 27; c = +165;
Δ = b2-4ac
Δ = 272-4·1·165
Δ = 69
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{69}}{2*1}=\frac{-27-\sqrt{69}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{69}}{2*1}=\frac{-27+\sqrt{69}}{2} $
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