F(-5)=x^2+3x-22

Solution for F(-5)=x^2+3x-22 equation:

(-5)=F^2+3F-22

We move all terms to the left:

(-5)-(F^2+3F-22)=0

We add all the numbers together, and all the variables

-(F^2+3F-22)-5=0

We get rid of parentheses

-F^2-3F+22-5=0

We add all the numbers together, and all the variables

-1F^2-3F+17=0

a = -1; b = -3; c = +17;
Δ = b2-4ac
Δ = -32-4·(-1)·17
Δ = 77
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{-(-3)-\sqrt{77}}{2*-1}=\frac{3-\sqrt{77}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{77}}{2*-1}=\frac{3+\sqrt{77}}{-2}
$