F(x)=x2-6x+8

Solution for F(x)=x2-6x+8 equation:

(F)=F2-6F+8

We move all terms to the left:

(F)-(F2-6F+8)=0

We add all the numbers together, and all the variables

-(+F^2-6F+8)+F=0

We get rid of parentheses

-F^2+6F+F-8=0

We add all the numbers together, and all the variables

-1F^2+7F-8=0

a = -1; b = 7; c = -8;
Δ = b2-4ac
Δ = 72-4·(-1)·(-8)
Δ = 17
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{-(7)-\sqrt{17}}{2*-1}=\frac{-7-\sqrt{17}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{17}}{2*-1}=\frac{-7+\sqrt{17}}{-2}
$