Question

How do you solve `27 x + 4 = 40 x ^2` using the quadratic formula?

Answer 1

`4/5 and (-1/8)`

Explanation:

Solve the quadratic equation:
`y = 40x^2 - 27x - 4 = 0`
Use the improved quadratic formula (Socratic Search)
`D = d^2 = b^2 - 4ac = 729 + 640 = 1369` --> `d = +- 37`
There are 2 real roots:
`x = -b/(2a) +- d/(2a) = 27/80 +- 37/80 = (27 +- 37)/80`
`x1 = 64/80 = 4/5`
`x2 = - 10/80 = - 1/8`