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

Mar 22, 2018

$\frac{3}{2}$, and -4

Explanation:

Solve it by the new Transforming Method (Socratic Search).
$y = 2 {x}^{2} + 5 x - 12 = 0$
Transformed equation:
$y ' = {x}^{2} + 5 x - 24 = 0.$
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:
$x 1 = \frac{3}{a} = \frac{3}{2}$, and $x 2 = - \frac{8}{a} = - \frac{8}{2} = - 4$

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