The Lorentz equation for working out time dilatation is actually very simple and is basically just pythagorus's right-angle triangle solution. Because of this, you can actually solve it by trigonometry, and as you've chosen a value for the degree of time dilation of 50%, which corresponds to sin(30°), the solution is simply cos(30°) = 0.866 * 'c' = 86.6% of the speed of light.