Solve 0.2v^2-0.0004v+500=y

$$0.2 v ^ { 2 } - 0.0004 v + 500 = y$$

Solve for y

$$y=\frac{v^{2}}{5}-\frac{v}{2500}+500$$

Solution Steps

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

$$y=0.2v^{2}-0.0004v+500$$

Solve for v (complex solution)

$$v=\frac{5\sqrt{\frac{4y}{5}-399.99999984}}{2}+0.001$$

$$v=-\frac{5\sqrt{\frac{4y}{5}-399.99999984}}{2}+0.001$$

Solve for v

$$v=\frac{5\sqrt{\frac{4y}{5}-399.99999984}}{2}+0.001$$

$$v=-\frac{5\sqrt{\frac{4y}{5}-399.99999984}}{2}+0.001\text{, }y\geq 499.9999998$$