9f^2=-16f

Solution for 9f^2=-16f equation:

9f^2=-16f

We move all terms to the left:

9f^2-(-16f)=0

We get rid of parentheses

9f^2+16f=0

a = 9; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·9·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*9}=\frac{-32}{18}
=-1+7/9
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*9}=\frac{0}{18}
=0
$