How do you solve #6m^2 = 13m + 28#?

1 Answer
Jun 28, 2015

Answer:

Solve #y = 6x^2 - 13x - 28 = 0# (1)

Explanation:

I use the new Transforming Method (see Google or Yahoo Search).
Transformed equation: #y' = x^2 - 13x - 168 = 0# (2). Roots have different signs (Rule of signs).
Factor pairs of (ac = - 168) -> (6, 28)(-8, 21). This sum is 13 = -b.
The 2 real roots of (2) are: X1 = -8 and X2 = 21.

Back to original equation (1), the 2 real roots are:

#x1 = X1/a = -8/6 = -4/3# and #x2 = X2/a = 21/6 = 7/2#