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(F)=-5F^2+14F+1
We move all terms to the left:
(F)-(-5F^2+14F+1)=0
We get rid of parentheses
5F^2-14F+F-1=0
We add all the numbers together, and all the variables
5F^2-13F-1=0
a = 5; b = -13; c = -1;
Δ = b2-4ac
Δ = -132-4·5·(-1)
Δ = 189
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}$$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-3\sqrt{21}}{2*5}=\frac{13-3\sqrt{21}}{10} $$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+3\sqrt{21}}{2*5}=\frac{13+3\sqrt{21}}{10} $
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