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4m^2+9m-55=0
a = 4; b = 9; c = -55;
Δ = b2-4ac
Δ = 92-4·4·(-55)
Δ = 961
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{961}=31$$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-31}{2*4}=\frac{-40}{8} =-5 $$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+31}{2*4}=\frac{22}{8} =2+3/4 $
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