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(F)=2F^2-5F-6
We move all terms to the left:
(F)-(2F^2-5F-6)=0
We get rid of parentheses
-2F^2+F+5F+6=0
We add all the numbers together, and all the variables
-2F^2+6F+6=0
a = -2; b = 6; c = +6;
Δ = b2-4ac
Δ = 62-4·(-2)·6
Δ = 84
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}$$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{21}}{2*-2}=\frac{-6-2\sqrt{21}}{-4} $$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{21}}{2*-2}=\frac{-6+2\sqrt{21}}{-4} $
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