F(x)=x2-8x+17

Solution for F(x)=x2-8x+17 equation:

(F)=F2-8F+17

We move all terms to the left:

(F)-(F2-8F+17)=0

We add all the numbers together, and all the variables

-(+F^2-8F+17)+F=0

We get rid of parentheses

-F^2+8F+F-17=0

We add all the numbers together, and all the variables

-1F^2+9F-17=0

a = -1; b = 9; c = -17;
Δ = b2-4ac
Δ = 92-4·(-1)·(-17)
Δ = 13
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{13}}{2*-1}=\frac{-9-\sqrt{13}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{13}}{2*-1}=\frac{-9+\sqrt{13}}{-2}
$