F(-3)=2x^2-9x-5

Solution for F(-3)=2x^2-9x-5 equation:

(-3)=2F^2-9F-5

We move all terms to the left:

(-3)-(2F^2-9F-5)=0

We add all the numbers together, and all the variables

-(2F^2-9F-5)-3=0

We get rid of parentheses

-2F^2+9F+5-3=0

We add all the numbers together, and all the variables

-2F^2+9F+2=0

a = -2; b = 9; c = +2;
Δ = b2-4ac
Δ = 92-4·(-2)·2
Δ = 97
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{-(9)-\sqrt{97}}{2*-2}=\frac{-9-\sqrt{97}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{97}}{2*-2}=\frac{-9+\sqrt{97}}{-4}
$