f2+8f=7

Solution for f2+8f=7 equation:

f2+8f=7

We move all terms to the left:

f2+8f-(7)=0

We add all the numbers together, and all the variables

f^2+8f-7=0

a = 1; b = 8; c = -7;
Δ = b2-4ac
Δ = 82-4·1·(-7)
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{23}}{2*1}=\frac{-8-2\sqrt{23}}{2}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{23}}{2*1}=\frac{-8+2\sqrt{23}}{2}
$