F(x)=-x^2+8x-7

Solution for F(x)=-x^2+8x-7 equation:

(F)=-F^2+8F-7

We move all terms to the left:

(F)-(-F^2+8F-7)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

F^2-7F+7=0

a = 1; b = -7; c = +7;
Δ = b2-4ac
Δ = -72-4·1·7
Δ = 21
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{21}}{2*1}=\frac{7-\sqrt{21}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{21}}{2*1}=\frac{7+\sqrt{21}}{2}
$