F(x)=-2x^2+54x-280

Solution for F(x)=-2x^2+54x-280 equation:

(F)=-2F^2+54F-280

We move all terms to the left:

(F)-(-2F^2+54F-280)=0

We get rid of parentheses

2F^2-54F+F+280=0

We add all the numbers together, and all the variables

2F^2-53F+280=0

a = 2; b = -53; c = +280;
Δ = b2-4ac
Δ = -532-4·2·280
Δ = 569
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{-(-53)-\sqrt{569}}{2*2}=\frac{53-\sqrt{569}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+\sqrt{569}}{2*2}=\frac{53+\sqrt{569}}{4}
$