Answer:
see explanation
Step-by-step explanation:
given
g(x) = 3x² - 5 then g(t) = 3t² - 5
Also g(t) = - [tex]\frac{7}{2}[/tex] t, hence
3t² - 5 = - [tex]\frac{7}{2}[/tex] t
multiply both sides by 2 to eliminate the fraction
6t² - 10 = - 7t ( add 7t to both sides )
6t² + 7t - 10 = 0 ← in standard form
(t + 2)(6t - 5) = 0 ← in factored form
Equate each factor to zero and solve for t
t + 2 = 0 ⇒ t = - 2
6t - 5 = 0 ⇒ t = [tex]\frac{5}{6}[/tex]
