F(1)=5,f(2)=8,f(3)=11,f(4)=14,f(5)=17

Solution for F(1)=5,f(2)=8,f(3)=11,f(4)=14,f(5)=17 equation:

(1)=5.F(2)=8.F(3)=11.F(4)=14.F(5)=17

We move all terms to the left:

(1)-(5.F(2))=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

-5.F^2+1=0

We add all the numbers together, and all the variables

-5F^2+1=0

a = -5; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-5)·1
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{5}}{2*-5}=\frac{0-2\sqrt{5}}{-10}
=-\frac{2\sqrt{5}}{-10}
=-\frac{\sqrt{5}}{-5}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{5}}{2*-5}=\frac{0+2\sqrt{5}}{-10}
=\frac{2\sqrt{5}}{-10}
=\frac{\sqrt{5}}{-5}
$