Basic Math Examples

$r t^{2} - s t = k$

Step 1

Subtract $k$ from both sides of the equation.

$r t^{2} - s t - k = 0$

Step 2

Use the quadratic formula to find the solutions.

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

Step 3

Substitute the values $a = r$ , $b = - s$ , and $c = - k$ into the quadratic formula and solve for $t$ .

$\frac{s \pm \sqrt{{(- s)}^{2} - 4 \cdot (r \cdot (- k))}}{2 r}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the product rule to $- s$ .

$t = \frac{s \pm \sqrt{{(- 1)}^{2} s^{2} - 4 \cdot r \cdot (- 1 k)}}{2 r}$

Step 4.2

Raise $- 1$ to the power of $2$ .

$t = \frac{s \pm \sqrt{1 s^{2} - 4 \cdot r \cdot (- 1 k)}}{2 r}$

Step 4.3

Multiply $s^{2}$ by $1$ .

$t = \frac{s \pm \sqrt{s^{2} - 4 \cdot r \cdot (- 1 k)}}{2 r}$

Step 4.4

Multiply $- 1$ by $- 4$ .

$t = \frac{s \pm \sqrt{s^{2} + 4 r k}}{2 r}$

Step 5

The final answer is the combination of both solutions.

$t = \frac{s + \sqrt{s^{2} + 4 r k}}{2 r}$

$t = \frac{s - \sqrt{s^{2} + 4 r k}}{2 r}$