[tex](3t^2-10)^2+5(3t^2-10)-14=0[/tex]
Suppose for the moment that you substitute [tex]u=3t^2-10[/tex]. Then the equation becomes
[tex]u^2+5u-14=0[/tex]
You could use the quadratic formula from this point, but no need, since you can easily factorize:
[tex]u^2+5u-14=(u+7)(u-2)=0\implies u=-7\text{ or }u=2[/tex]
This in turn means
[tex]3t^2-10=-7\text{ or }3t^2-10=2[/tex]
Can you solve for [tex]t[/tex] from here?
