Question

What is the quadratic formula for (3t^(2)-10)^(2)+5(3t^(2)-10)-14=0 ?

With work would be appreciated please. I'm trying to learn this, but im struggling

Answer 1

`(3t^2-10)^2+5(3t^2-10)-14=0`

Suppose for the moment that you substitute
`u=3t^2-10`. Then the equation becomes

`u^2+5u-14=0`

You could use the quadratic formula from this point, but no need, since you can easily factorize:

`u^2+5u-14=(u+7)(u-2)=0\implies u=-7\text{ or }u=2`

This in turn means

`3t^2-10=-7\text{ or }3t^2-10=2`

Can you solve for
`t` from here?