Solve 3w=(v+1)^2/2

$$3 w = \frac { ( v + 1 ) ^ { 2 } } { 2 }$$

Solve for w

$$w=\frac{\left(v+1\right)^{2}}{6}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$6w=\left(v+1\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(v+1\right)^{2}.

$$6w=v^{2}+2v+1$$

Divide both sides by 6.

$$\frac{6w}{6}=\frac{\left(v+1\right)^{2}}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$w=\frac{\left(v+1\right)^{2}}{6}$$

Solve for v (complex solution)

$$v=-\left(\sqrt{6w}+1\right)$$

$$v=\sqrt{6w}-1$$

Solve for v

$$v=-\left(\sqrt{6w}+1\right)$$

$$v=\sqrt{6w}-1\text{, }w\geq 0$$