Solve

w^2+3w-54=0

x= -1 minus sqrt55, -1+ plus sqrt55

Is this right?

(w+9)(w-6) = 0

w = -9 or w = +6

using your formula

-3/2 +/- (1/2)sqrt(9 + 216)
= -1.5 +/- .5 sqrt (225)
but 225 = 15 * 15
so
-1.5 +/- 7.5
- 9 or + 6
which we knew of course

To solve the quadratic equation w^2 + 3w - 54 = 0, you can use the quadratic formula. The quadratic formula is given by:

w = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a = 1, b = 3, and c = -54. Substituting these values into the quadratic formula, we get:

w = (-(3) ± √((3)^2 - 4(1)(-54))) / (2(1))

Simplifying further:

w = (-3 ± √(9 + 216)) / 2

w = (-3 ± √(225)) / 2

w = (-3 ± 15) / 2

This gives us two possible solutions:

w = (-3 - 15) / 2 = -18 / 2 = -9
w = (-3 + 15) / 2 = 12 / 2 = 6

Therefore, the correct solutions to the quadratic equation w^2 + 3w - 54 = 0 are w = -9 and w = 6.

The values x = -1 - √55 and x = -1 + √55 seem to be irrelevant to the given equation and are not correct solutions.