Solve -1/5m^2-21/10n-4=0

$$- \frac { 1 } { 5 } m ^ { 2 } - \frac { 21 } { 10 } n - 4 = 0$$

Solve for n

$$n=\frac{-2m^{2}-40}{21}$$

Steps for Solving Linear Equation

Add \frac{1}{5}m^{2} to both sides. Anything plus zero gives itself.

$$-\frac{21}{10}n-4=\frac{1}{5}m^{2}$$

Add 4 to both sides.

$$-\frac{21}{10}n=\frac{1}{5}m^{2}+4$$

The equation is in standard form.

$$-\frac{21}{10}n=\frac{m^{2}}{5}+4$$

Divide both sides of the equation by -\frac{21}{10}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{21}{10}n}{-\frac{21}{10}}=\frac{\frac{m^{2}}{5}+4}{-\frac{21}{10}}$$

Dividing by -\frac{21}{10} undoes the multiplication by -\frac{21}{10}.

$$n=\frac{\frac{m^{2}}{5}+4}{-\frac{21}{10}}$$

Divide \frac{m^{2}}{5}+4 by -\frac{21}{10} by multiplying \frac{m^{2}}{5}+4 by the reciprocal of -\frac{21}{10}.

$$n=\frac{-2m^{2}-40}{21}$$

Solve for m (complex solution)

$$m=-\frac{\sqrt{-42n-80}}{2}$$

$$m=\frac{\sqrt{-42n-80}}{2}$$

Solve for m

$$m=\frac{\sqrt{-42n-80}}{2}$$

$$m=-\frac{\sqrt{-42n-80}}{2}\text{, }n\leq -\frac{40}{21}$$