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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

5F^2-7F-2=0

a = 5; b = -7; c = -2;
Δ = b2-4ac
Δ = -72-4·5·(-2)
Δ = 89
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{89}}{2*5}=\frac{7-\sqrt{89}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{89}}{2*5}=\frac{7+\sqrt{89}}{10}
$