Solve 3t^2-2sqrt{3}t+1d=0

$$3 t ^ { 2 } - 2 \sqrt { 3 } t + 1 d = 0$$

Solve for d

$$d=t\left(-3t+2\sqrt{3}\right)$$

Solution Steps

Subtract 3t^{2}-2\sqrt{3}t from both sides. Anything subtracted from zero gives its negation.

$$1d=-\left(3t^{2}-2\sqrt{3}t\right)$$

Reorder the terms.

$$d=-\left(3t^{2}-2\sqrt{3}t\right)$$

To find the opposite of 3t^{2}-2\sqrt{3}t, find the opposite of each term.

$$d=-3t^{2}+2\sqrt{3}t$$

Solve for t

$$t=-\frac{\sqrt{3}\left(\sqrt{1-d}-1\right)}{3}$$

$$t=\frac{\sqrt{3}\left(\sqrt{1-d}+1\right)}{3}\text{, }d\leq 1$$