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2k^2-5k-18=9
We move all terms to the left:
2k^2-5k-18-(9)=0
We add all the numbers together, and all the variables
2k^2-5k-27=0
a = 2; b = -5; c = -27;
Δ = b2-4ac
Δ = -52-4·2·(-27)
Δ = 241
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}$$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{241}}{2*2}=\frac{5-\sqrt{241}}{4} $$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{241}}{2*2}=\frac{5+\sqrt{241}}{4} $
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