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5k^2+54k+117=0
a = 5; b = 54; c = +117;
Δ = b2-4ac
Δ = 542-4·5·117
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{576}=24$$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-24}{2*5}=\frac{-78}{10} =-7+4/5 $$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+24}{2*5}=\frac{-30}{10} =-3 $
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