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(F)=F^2+12F-69
We move all terms to the left:
(F)-(F^2+12F-69)=0
We get rid of parentheses
-F^2+F-12F+69=0
We add all the numbers together, and all the variables
-1F^2-11F+69=0
a = -1; b = -11; c = +69;
Δ = b2-4ac
Δ = -112-4·(-1)·69
Δ = 397
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{-(-11)-\sqrt{397}}{2*-1}=\frac{11-\sqrt{397}}{-2} $$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{397}}{2*-1}=\frac{11+\sqrt{397}}{-2} $
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