F(x)=-2x^2+12x+54

Solution for F(x)=-2x^2+12x+54 equation:

(F)=-2F^2+12F+54

We move all terms to the left:

(F)-(-2F^2+12F+54)=0

We get rid of parentheses

2F^2-12F+F-54=0

We add all the numbers together, and all the variables

2F^2-11F-54=0

a = 2; b = -11; c = -54;
Δ = b2-4ac
Δ = -112-4·2·(-54)
Δ = 553
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{553}}{2*2}=\frac{11-\sqrt{553}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{553}}{2*2}=\frac{11+\sqrt{553}}{4}
$