.
Your starting equation is
x^2 - 7x - 30 = 0
It is easy to factor:
the leading coefficient is 1;
30 is the product of 3 and 10;
you should have it with the " - " sign;
and -10 and 3 sum up to -7,
so, in factored form, the equation is
(x-10)*(x+3) = 0.
Obviously, it has the roots 10 and -3.
Solved.
I think, the necessary time to get it solved in your head is from 10 to 20 seconds,
depending on your experience.
----------------
In order for to see many other similar solved problems and to develop your experience, look into my lesson
- Solving quadratic equations without quadratic formula
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this textbook under the topic "Quadratic equations".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
Happy learning (!)