F(-1)=2x^2+5x-17

Solution for F(-1)=2x^2+5x-17 equation:

(-1)=2F^2+5F-17

We move all terms to the left:

(-1)-(2F^2+5F-17)=0

We add all the numbers together, and all the variables

-(2F^2+5F-17)-1=0

We get rid of parentheses

-2F^2-5F+17-1=0

We add all the numbers together, and all the variables

-2F^2-5F+16=0

a = -2; b = -5; c = +16;
Δ = b2-4ac
Δ = -52-4·(-2)·16
Δ = 153
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{17}}{2*-2}=\frac{5-3\sqrt{17}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{17}}{2*-2}=\frac{5+3\sqrt{17}}{-4}
$