Solve T=sqrt{g+6/2}

$$T = \sqrt { \frac { g + 6 } { 2 } }$$

Solve for g

$$g=2\left(T^{2}-3\right)$$

$$T\geq 0$$

Steps for Solving Radical Equations

Divide each term of g+6 by 2 to get \frac{1}{2}g+3.

$$T=\sqrt{\frac{1}{2}g+3}$$

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{\frac{1}{2}g+3}=T$$

Square both sides of the equation.

$$\frac{1}{2}g+3=T^{2}$$

Subtract 3 from both sides of the equation.

$$\frac{1}{2}g+3-3=T^{2}-3$$

Subtracting 3 from itself leaves 0.

$$\frac{1}{2}g=T^{2}-3$$

Multiply both sides by 2.

$$\frac{\frac{1}{2}g}{\frac{1}{2}}=\frac{T^{2}-3}{\frac{1}{2}}$$

Dividing by \frac{1}{2} undoes the multiplication by \frac{1}{2}.

$$g=\frac{T^{2}-3}{\frac{1}{2}}$$

Divide T^{2}-3 by \frac{1}{2} by multiplying T^{2}-3 by the reciprocal of \frac{1}{2}.

$$g=2T^{2}-6$$

Solve for T

$$T=\frac{\sqrt{2\left(g+6\right)}}{2}$$

$$g\geq -6$$