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 = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{26}}{2*-1}=\frac{8-2\sqrt{26}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{26}}{2*-1}=\frac{8+2\sqrt{26}}{-2}
$