Question

Solve for tS=9t^2-vt

Answer 1

`t=\frac{v+\sqrt[]{v^2+36S}}{18},\frac{v-\sqrt[]{v^2+36S}}{18}`

Explanation:

We have the following equation:

`S=9t^2-vt\:`

We solve for t:

`9t^2-vt-S=0`

We can solve by means of the general equation of the quadratic formulas.

Knowing that:

a = 9

b = -v

c = -S

`\begin{gathered} t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{ Replacing:} \\ t=\frac{-(-v)\pm\sqrt[]{(-v)^2-4\cdot9\cdot(-S)}}{2\cdot9}=\frac{v\pm\sqrt[]{v^2+36S}}{18} \\ t_1=\frac{v+\sqrt[]{v^2+36S}}{18} \\ t_2=\frac{v-\sqrt[]{v^2+36S}}{18} \end{gathered}`