Equation Manipulation with Differentiation or Integration?

[Stuart Caffre]

Solve the equation below to gain an expression for θ(t), where v, β and r₀ are constants and the only variables are time(t) and theta(θ):

vt=r₀θ+βθ²/2

The exercise is based upon the spiral data track of a compact disc and either side of the equation is equal to the displacement. I’ve tried manipulating the equation to no avail and expect two possible answers but am unsure how to proceed and would very much appreciate any guidance with this.

 

[mathman]

It looks like an elementary quadratic.

θ=(-r ± √(r² + 2vtβ) )/β

 

[Stuart Caffre]

Thanks Mathman and apologies for posting this in the wrong area it won't happen again, and your help is greatly appreciated by a mature student whose grey cells seem to be white