Answer:
[tex]t = -7\ \ \ or\ \ t = 10[/tex]
Step-by-step explanation:
Given
[tex]f(t) = 2t^2 - 6t[/tex]
Required
Find t, when [tex]f(t) = 140[/tex]
Substitute 140 for f(t) in [tex]f(t) = 2t^2 - 6t[/tex]
[tex]140 = 2t^2 - 6t[/tex]
Divide through by 2
[tex]\frac{140}{2} = \frac{2t^2 - 6t}{2}[/tex]
[tex]70 = t^2 - 3t[/tex]
[tex]t^2 - 3t = 70[/tex]
Subtract 70 from both sides
[tex]t^2 - 3t - 70= 70 - 70[/tex]
[tex]t^2 - 3t - 70= 0[/tex]
Expand
[tex]t^2 -10t + 7t - 70 = 0[/tex]
Factorize:
[tex]t(t - 10) + 7(t - 10) = 0[/tex]
[tex](t + 7)(t - 10) = 0[/tex]
Split:
[tex]t + 7 = 0\ \ \ or\ \ t - 10 = 0[/tex]
[tex]t = -7\ \ \ or\ \ t = 10[/tex]
Hence, the values of t are -7 and 10
