F(x)=-4x^2+8x+5

Solution for F(x)=-4x^2+8x+5 equation:

(F)=-4F^2+8F+5

We move all terms to the left:

(F)-(-4F^2+8F+5)=0

We get rid of parentheses

4F^2-8F+F-5=0

We add all the numbers together, and all the variables

4F^2-7F-5=0

a = 4; b = -7; c = -5;
Δ = b2-4ac
Δ = -72-4·4·(-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*4}=\frac{7-\sqrt{129}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{129}}{2*4}=\frac{7+\sqrt{129}}{8}
$