How do you solve  t^2- t/6= 35/6?

Sep 6, 2016

Multiply through by 6, move all terms to one side, factor, and solve.

Explanation:

Multiply both sides of the equation by 6, to get rid of the denominator of 6.

$6 \left({t}^{2} - \frac{t}{6}\right) = 6 \left(\frac{35}{6}\right)$

$6 {t}^{2} - t = 35$

To get all the terms on one side, subtract 35 from both sides of the equation.
$6 {t}^{2} - t - 35 = 0$

Factor.
$\left(3 t + 7\right) \left(2 t - 5\right) = 0$

Set each factor equal to zero.
$3 t + 7 = 0$
$2 t - 5 = 0$

Solve for t.

For the first equation, subtract 7 from both sides.
$3 t = - 7$

Then divide both sides by 3.

$t = - \frac{7}{3}$

Solve $2 t - 5 = 0$ by adding 5 to both sides and then dividing both sides by 2: which results in $t = \frac{5}{2}$.