Solve m^2+m+4q=0

$$m ^ { 2 } + m + 4 q = 0$$

Solve for q

$$q=-\frac{m\left(m+1\right)}{4}$$

Steps for Solving Linear Equation

Subtract m^{2} from both sides. Anything subtracted from zero gives its negation.

$$m+4q=-m^{2}$$

Subtract m from both sides.

$$4q=-m^{2}-m$$

Divide both sides by 4.

$$\frac{4q}{4}=-\frac{m\left(m+1\right)}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$q=-\frac{m\left(m+1\right)}{4}$$

Solve for m (complex solution)

$$m=\frac{\sqrt{1-16q}-1}{2}$$

$$m=\frac{-\sqrt{1-16q}-1}{2}$$

Solve for m

$$m=\frac{\sqrt{1-16q}-1}{2}$$

$$m=\frac{-\sqrt{1-16q}-1}{2}\text{, }q\leq \frac{1}{16}$$