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

1 Answer
Jun 30, 2015

Answer:

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.