Question

How do you solve `2x^2+5x-12=0`?

Answer 1

`3/2`, and -4

Explanation:

Solve it by the new Transforming Method (Socratic Search).
`y = 2x^2 + 5x - 12 = 0`
Transformed equation:
`y' = x^2 + 5x - 24 = 0.`
Proceeding. Find the 2 real roots of y', then, divide them by a = 2.
Find 2 real roots knowing the sum (-b = -5) and the product
(ac = -24).
They are 3, and -8.
The 2 real roots of y are:
`x1 = 3/a = 3/2`, and `x2 = -8/a = -8/2 = -4`

Note . This method avoids the lengthy factoring by grouping and solving the 2 binomials.