F(-3)=2x2+5x-9

Solution for F(-3)=2x2+5x-9 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2F^2-5F+6=0

a = -2; b = -5; c = +6;
Δ = b2-4ac
Δ = -52-4·(-2)·6
Δ = 73
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{-(-5)-\sqrt{73}}{2*-2}=\frac{5-\sqrt{73}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{73}}{2*-2}=\frac{5+\sqrt{73}}{-4}
$