Question

How do you solve `-4x^2+19x=-30`?

Answer 1

`x=6` or `x=-5/4`

Explanation:

Bring the equation to standard form:
y = 4x^2 - 19x - 30 = 0
Use the improved quadratic formula (Socratic Search)
`D = d^2 = b^2 - 4ac = 361 + 480 = 841` --> `d = +- 29`
There are 2 real roots:
`x = -b/(2a) +- d/(2a) = 19/8 +- 29/8`
`x = (19 +- 29)/8`

i.e. `x=6` or `x=-5/4`