Solve 3tg^2x-1=0

$$3 t g ^ { 2 } x - 1 = 0$$

Solve for t

$$t=\frac{1}{3xg^{2}}$$

$$x\neq 0\text{ and }g\neq 0$$

Steps for Solving Linear Equation

Add 1 to both sides. Anything plus zero gives itself.

$$3tg^{2}x=1$$

The equation is in standard form.

$$3xg^{2}t=1$$

Divide both sides by 3g^{2}x.

$$\frac{3xg^{2}t}{3xg^{2}}=\frac{1}{3xg^{2}}$$

Dividing by 3g^{2}x undoes the multiplication by 3g^{2}x.

$$t=\frac{1}{3xg^{2}}$$

Solve for g (complex solution)

$$g=-\frac{\sqrt{3}t^{-\frac{1}{2}}x^{-\frac{1}{2}}}{3}$$

$$g=\frac{\sqrt{3}t^{-\frac{1}{2}}x^{-\frac{1}{2}}}{3}\text{, }x\neq 0\text{ and }t\neq 0$$

Solve for g

$$g=\frac{\sqrt{\frac{3}{tx}}}{3}$$

$$g=-\frac{\sqrt{\frac{3}{tx}}}{3}\text{, }\left(x>0\text{ and }t>0\right)\text{ or }\left(t<0\text{ and }x<0\right)$$