w(3w-1)=200 solve for w

To solve the equation w(3w - 1) = 200, we can follow these steps:

Step 1: Expand the equation by multiplying w with the terms inside the parentheses:
3w^2 - w = 200

Step 2: Rearrange the equation to bring all the terms to one side and set it equal to zero:
3w^2 - w - 200 = 0

Step 3: Now we need to solve this quadratic equation. There are multiple methods to handle quadratic equations, but let's use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / 2a

In our equation, a = 3, b = -1, and c = -200.

Step 4: Plug in the values of a, b, and c into the quadratic formula to find the solutions for w:

w = (-(-1) ± √((-1)^2 - 4 * 3 * -200)) / (2 * 3)
w = (1 ± √(1 + 2400)) / 6
w = (1 ± √2401) / 6

Step 5: Simplify the expression:
w = (1 ± 49) / 6

This gives us two possible solutions:
w1 = (1 + 49) / 6 = 50 / 6 = 25/3
w2 = (1 - 49) / 6 = -48 / 6 = -8

So the solutions to the equation w(3w - 1) = 200 are w = 25/3 and w = -8.