Question

How do you solve the equation: `4x^2+13x-75=0`?

Answer 1

Solve `y = 4x^2 + 13x - 75 = 0` (1)

Explanation:

I use the new Transforming Method (Google, Yahoo Search)
Transformed equation `y' = x^2 + 13x - 300 = 0` (2). Roots have different signs.
Factor pairs of ac = -300 ->.... (-10, 30)(-12, 25). This sum is 13 = b. Then, the 2 real roots of (2) are: y1 = 12 and y2 = -25. Back to original equation (1), the 2 real roots are: `x1 = (y1)/a = 12/4 = 3`, and
`x2 = (y2)/a = - 25/4.`.
This method is fast, systematic. There are no factoring by grouping, and no solving binomials.