F(x)=x2-7x+1

Solution for F(x)=x2-7x+1 equation:

(F)=F2-7F+1

We move all terms to the left:

(F)-(F2-7F+1)=0

We add all the numbers together, and all the variables

-(+F^2-7F+1)+F=0

We get rid of parentheses

-F^2+7F+F-1=0

We add all the numbers together, and all the variables

-1F^2+8F-1=0

a = -1; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·(-1)·(-1)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{15}}{2*-1}=\frac{-8-2\sqrt{15}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{15}}{2*-1}=\frac{-8+2\sqrt{15}}{-2}
$