Question

How do you determine the solutions to `3x^2+10x-5=0`?

Answer 1

`(-10 +- 2sqrt10)/3`

Explanation:

Use the improved quadratic formula (Socratic Search)
`y = 3x^2 + 10x - 5 = 0`
`D = d^2 = b^2 - 4ac = 100 + 60 = 160` --> `d = +- 4sqrt10`
There are 2 real roots:
`x = -b/(2a) +- d/(2a) = -20/6 +- (4sqrt10)/6 = (-10 +- 2sqrt10)/3`