F(-5)=x2+2x-10

Solution for F(-5)=x2+2x-10 equation:

(-5)=F2+2F-10

We move all terms to the left:

(-5)-(F2+2F-10)=0

We add all the numbers together, and all the variables

-(+F^2+2F-10)+(-5)=0

We add all the numbers together, and all the variables

-(+F^2+2F-10)-5=0

We get rid of parentheses

-F^2-2F+10-5=0

We add all the numbers together, and all the variables

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

a = -1; b = -2; c = +5;
Δ = b2-4ac
Δ = -22-4·(-1)·5
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{6}}{2*-1}=\frac{2-2\sqrt{6}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{6}}{2*-1}=\frac{2+2\sqrt{6}}{-2}
$