f(f-9)=-15

Solution for f(f-9)=-15 equation:

f(f-9)=-15

We move all terms to the left:

f(f-9)-(-15)=0

We add all the numbers together, and all the variables

f(f-9)+15=0

We multiply parentheses

f^2-9f+15=0

a = 1; b = -9; c = +15;
Δ = b2-4ac
Δ = -92-4·1·15
Δ = 21
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{-(-9)-\sqrt{21}}{2*1}=\frac{9-\sqrt{21}}{2}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{21}}{2*1}=\frac{9+\sqrt{21}}{2}
$