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14k^2+5k-24=0
a = 14; b = 5; c = -24;
Δ = b2-4ac
Δ = 52-4·14·(-24)
Δ = 1369
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{1369}=37$$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-37}{2*14}=\frac{-42}{28} =-1+1/2 $$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+37}{2*14}=\frac{32}{28} =1+1/7 $
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