F(x)=(x+8)(8-x)

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

(F)=(F+8)(8-F)

We move all terms to the left:

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

We add all the numbers together, and all the variables

F-((F+8)(-1F+8))=0

We multiply parentheses ..

-((-1F^2+8F-8F+64))+F=0


We calculate terms in parentheses: -((-1F^2+8F-8F+64)), so:

(-1F^2+8F-8F+64)

We get rid of parentheses

-1F^2+8F-8F+64

We add all the numbers together, and all the variables

-1F^2+64

Back to the equation:

-(-1F^2+64)


We get rid of parentheses

1F^2+F-64=0

We add all the numbers together, and all the variables

F^2+F-64=0

a = 1; b = 1; c = -64;
Δ = b2-4ac
Δ = 12-4·1·(-64)
Δ = 257
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{-(1)-\sqrt{257}}{2*1}=\frac{-1-\sqrt{257}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{257}}{2*1}=\frac{-1+\sqrt{257}}{2}
$