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(F)=-16F^2+56F+3
We move all terms to the left:
(F)-(-16F^2+56F+3)=0
We get rid of parentheses
16F^2-56F+F-3=0
We add all the numbers together, and all the variables
16F^2-55F-3=0
a = 16; b = -55; c = -3;
Δ = b2-4ac
Δ = -552-4·16·(-3)
Δ = 3217
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}$$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-\sqrt{3217}}{2*16}=\frac{55-\sqrt{3217}}{32} $$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+\sqrt{3217}}{2*16}=\frac{55+\sqrt{3217}}{32} $
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