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

1 Answer
Sep 6, 2016

Answer:

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(t^2 - t/6) = 6(35/6)#

#6t^2 -t= 35#

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

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

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

Solve for t.

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

Then divide both sides by 3.

#t= -7/3#

Solve #2t-5=0# by adding 5 to both sides and then dividing both sides by 2: which results in #t=5/2#.