F(5)=5x^2+10x-1

Solution for F(5)=5x^2+10x-1 equation:

(5)=5F^2+10F-1

We move all terms to the left:

(5)-(5F^2+10F-1)=0

We get rid of parentheses

-5F^2-10F+1+5=0

We add all the numbers together, and all the variables

-5F^2-10F+6=0

a = -5; b = -10; c = +6;
Δ = b2-4ac
Δ = -102-4·(-5)·6
Δ = 220
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{55}}{2*-5}=\frac{10-2\sqrt{55}}{-10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{55}}{2*-5}=\frac{10+2\sqrt{55}}{-10}
$