Solving a Cubic Equation: How to Find the Real Root

[xzibition8612]

Homework Statement

2t^3-4t-5=0
Find t

Homework Equations

[-b-sqrt(b^2-4ac)]/2a

The Attempt at a Solution

The answer is sqrt(2/3). No idea how this came about. I tried plugging in the equation and got it wrong. :( Please help I've been struggling over this for 5 hours.

 

[Mentallic]

The quadratic formula

$$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$

Is only for quadratics. That is, equations of the form

$$y=ax^2+bx+c$$

But what you have is a cubic, so you can't use the quadratic formula. The cubic formula is way too complicated though, so we have other methods of going about solving them, such as the rational root theorem.

But now that I look at it, are you sure you wrote the cubic down correctly? The real root definitely isn't $\sqrt{2/3}$.