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5m^2-2m-24=0
a = 5; b = -2; c = -24;
Δ = b2-4ac
Δ = -22-4·5·(-24)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{484}=22$$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-22}{2*5}=\frac{-20}{10} =-2 $$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+22}{2*5}=\frac{24}{10} =2+2/5 $
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