F(x)=-8x^2+8x+2,5

Solution for F(x)=-8x^2+8x+2,5 equation:

(F)=-8F^2+8F+2.5

We move all terms to the left:

(F)-(-8F^2+8F+2.5)=0

We get rid of parentheses

8F^2-8F+F-2.5=0

We add all the numbers together, and all the variables

8F^2-7F-2.5=0

a = 8; b = -7; c = -2.5;
Δ = b2-4ac
Δ = -72-4·8·(-2.5)
Δ = 129
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{129}}{2*8}=\frac{7-\sqrt{129}}{16}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{129}}{2*8}=\frac{7+\sqrt{129}}{16}
$