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5k^2+k-42=0
a = 5; b = 1; c = -42;
Δ = b2-4ac
Δ = 12-4·5·(-42)
Δ = 841
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{841}=29$$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-29}{2*5}=\frac{-30}{10} =-3 $$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+29}{2*5}=\frac{28}{10} =2+4/5 $
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