How do you solve # 3x^2 - 14x - 5 = 0#?
You could solve this quadratic equation by using the quadratic formula.
For a quadratic equation that takes the general form
#color(blue)(ax^2 + bx + c = 0)#
the two solutions can be determined by using the quadratic formula
#color(blue)(x_(1,2) = (-b +- sqrt(b^2 - 4ac))/(2a)#
In your case,
Solve y = 3x^2 - 14x - 5 = 0 (1)
Ans: (- 1/3) and (5).
I use the new Transforming Method.
Transformed y' = x^2 - 14x - 15 = 0. (2)
Since (a -b + c = 0) --> 2 real roots of (2) are (-1) and (-c/a = 15).
Back to equation (1), the 2 real roots are: