I think you mean the quadratic formula x=(-b±√(b2-4ac))/2a.
In the given quadratic a=15, b=-7, c=-2.
b2=49; ac=15×(-2)=-30, 4ac=-120.
b2-4ac=49-(-120)=49+120=169 (=132).
√(b2-4ac)=13, x=(7±13)/30=(7+13)/30=20/30=⅔; or, (7-13)/30=-6/30=-⅕.
These are rational solutions so the quadratic can be factorised.
Since x=⅔ is a zero of the quadratic, 3x=2 making 3x-2 a factor.
The other factor is when x=-⅕, so x+⅕=0 and 5x+1 is the other factor.
(3x-2)(5x+1)=15x2+3x-10x-2=15x2-7x-2, the original quadratic expression.