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24f^2+55f-24=0
a = 24; b = 55; c = -24;
Δ = b2-4ac
Δ = 552-4·24·(-24)
Δ = 5329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{5329}=73$$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-73}{2*24}=\frac{-128}{48} =-2+2/3 $$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+73}{2*24}=\frac{18}{48} =3/8 $
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