-f(f+85)=5

Solution for -f(f+85)=5 equation:

-f(f+85)=5

We move all terms to the left:

-f(f+85)-(5)=0

We multiply parentheses

-f^2-85f-5=0

We add all the numbers together, and all the variables

-1f^2-85f-5=0

a = -1; b = -85; c = -5;
Δ = b2-4ac
Δ = -852-4·(-1)·(-5)
Δ = 7205
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{-(-85)-\sqrt{7205}}{2*-1}=\frac{85-\sqrt{7205}}{-2}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-85)+\sqrt{7205}}{2*-1}=\frac{85+\sqrt{7205}}{-2}
$