F(x)=-x2+8x=14

Solution for F(x)=-x2+8x=14 equation:

(F)=-F2+8F=14

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

1F^2-8F+F=0

We add all the numbers together, and all the variables

F^2-7F=0

a = 1; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·1·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*1}=\frac{0}{2}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*1}=\frac{14}{2}
=7
$