I can't find the numbers that when I multiply it gives me 7 and when are added gives me a 6....

Did my tutor make a mistake with the numbers or I'm tripping?

Please be kind I know I'm stupid.
Use the quadratic formula to get the 2 irrational roots in exact form
There are not two integers which will multiply to give 7 and add to give 6. I suggest you check with your tutor. When I solve this on my calculator I get t=-4.41 or t=-1.59 (rounded to two decimal places)
Maybe you copied it down wrong, switching the 6 and the 7?
t^2 + 7t + 6 would be the more commonly used problem for factoring practice.
If the equation were

t² + 6t - 7 = 0

or equivalent

t² + 6t = 7

The solutions are integers. Maybe is a typo.

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other similar equations with integer solutions:

t² + 7t + 6 = 0

t² - 7t + 6 = 0
As others have said it is not practical to solve this by factorising. It’s either a mistake (-7 is 7*-1.  7+-1 is 6) or it’s there to make you realise that you need another method for some quadratics or you’ve already been taught another method and they want you to use that (either Completing the square, the equation or drawing the graph to get approximate solutions)