Basic Math Examples

$d = v t + a t^{2}$

Step 1

Rewrite the equation as $v t + a t^{2} = d$ .

$v t + a t^{2} = d$

Step 2

Subtract $d$ from both sides of the equation.

$v t + a t^{2} - d = 0$

Step 3

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 4

Substitute the values $a = a$ , $b = v$ , and $c = - d$ into the quadratic formula and solve for $t$ .

$\frac{- v \pm \sqrt{v^{2} - 4 \cdot (a \cdot (- d))}}{2 a}$

Step 5

Multiply $- 1$ by $- 4$ .

$t = \frac{- v \pm \sqrt{v^{2} + 4 a d}}{2 a}$

Step 6

The final answer is the combination of both solutions.

$t = - \frac{v - \sqrt{v^{2} + 4 a d}}{2 a}$

$t = - \frac{v + \sqrt{v^{2} + 4 a d}}{2 a}$