How do you solve $t^{2} - \frac{t}{6} = \frac{35}{6}$ $t^2- t/6= 35/6$ ?

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Answer 1 · 2016-09-06T18:10:08

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

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

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

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

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

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

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

Solve for t.

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

Then divide both sides by 3.

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

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

How do you solve t^2- t/6= 35/6t2−t6=356 t^2- t/6= 35/6?