Question

How do you solve `30x² + 5x - 10 = 0`?

Answer 1

Solve `y = 30x^2 + 5x - 10 = 0` (1)

Ans: `1/2 and (-2/3)`

Explanation:

I use the new Transforming Method (Google, Yahoo Search).
Transformed equation: `y' = x^2 + 5x - 300 = 0` (2).
Roots have opposite signs (Rule of signs).
Factor pairs of (-300): ...(-10, 30)(-15, 20). This sum is 5 = b. Then the 2 real roots of (2) are the opposite: y1 = 15 and y2 = -20 .
Back to original equation (1), the 2 real roots are: `x1 = (y1)/a = 15/30 = 1/2`, and `x2 = (y2)/a = -20/30 = -2/3`

NOTE. This method avoid the lengthy factoring by grouping and solving the 2 binomials.