F(0)=x^2-8x+10

Solution for F(0)=x^2-8x+10 equation:

(0)=F^2-8F+10

We move all terms to the left:

(0)-(F^2-8F+10)=0

We add all the numbers together, and all the variables

-(F^2-8F+10)=0

We get rid of parentheses

-F^2+8F-10=0

We add all the numbers together, and all the variables

-1F^2+8F-10=0

a = -1; b = 8; c = -10;
Δ = b2-4ac
Δ = 82-4·(-1)·(-10)
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{-(8)-2\sqrt{6}}{2*-1}=\frac{-8-2\sqrt{6}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{6}}{2*-1}=\frac{-8+2\sqrt{6}}{-2}
$