F(x)=-2x^2-12x+5

Solution for F(x)=-2x^2-12x+5 equation:

(F)=-2F^2-12F+5

We move all terms to the left:

(F)-(-2F^2-12F+5)=0

We get rid of parentheses

2F^2+12F+F-5=0

We add all the numbers together, and all the variables

2F^2+13F-5=0

a = 2; b = 13; c = -5;
Δ = b2-4ac
Δ = 132-4·2·(-5)
Δ = 209
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{-(13)-\sqrt{209}}{2*2}=\frac{-13-\sqrt{209}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{209}}{2*2}=\frac{-13+\sqrt{209}}{4}
$