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

Solution for F(x)=x^2+7x-1 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1F^2-6F+1=0

a = -1; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·(-1)·1
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{10}}{2*-1}=\frac{6-2\sqrt{10}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{10}}{2*-1}=\frac{6+2\sqrt{10}}{-2}
$