7f^2=f+1

Solution for 7f^2=f+1 equation:

7f^2=f+1

We move all terms to the left:

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

We get rid of parentheses

7f^2-f-1=0

We add all the numbers together, and all the variables

7f^2-1f-1=0

a = 7; b = -1; c = -1;
Δ = b2-4ac
Δ = -12-4·7·(-1)
Δ = 29
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{-(-1)-\sqrt{29}}{2*7}=\frac{1-\sqrt{29}}{14}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{29}}{2*7}=\frac{1+\sqrt{29}}{14}
$