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-kx+4=-9x^{2}
Subtract 9x^{2} from both sides. Anything subtracted from zero gives its negation.
-kx=-9x^{2}-4
Subtract 4 from both sides.
\left(-x\right)k=-9x^{2}-4
The equation is in standard form.
\frac{\left(-x\right)k}{-x}=\frac{-9x^{2}-4}{-x}
Divide both sides by -x.
k=\frac{-9x^{2}-4}{-x}
Dividing by -x undoes the multiplication by -x.
k=9x+\frac{4}{x}
Divide -9x^{2}-4 by -x.