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(F)=12F^2-2
We move all terms to the left:
(F)-(12F^2-2)=0
We get rid of parentheses
-12F^2+F+2=0
a = -12; b = 1; c = +2;
Δ = b2-4ac
Δ = 12-4·(-12)·2
Δ = 97
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{-(1)-\sqrt{97}}{2*-12}=\frac{-1-\sqrt{97}}{-24} $$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{97}}{2*-12}=\frac{-1+\sqrt{97}}{-24} $
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