y^2-3y=54 what is y?

y= -6 or 9

thanks!

To find the value of y in the equation y^2 - 3y = 54, we can rearrange it into a quadratic equation and solve for y.

Step 1: Rewrite the equation in the standard quadratic form by moving all terms to one side of the equation:
y^2 - 3y - 54 = 0

Step 2: Factor the quadratic equation if possible. In this case, the equation does not factor easily, so we move to step 3.

Step 3: Use the quadratic formula to solve for y. The quadratic formula is given by:
y = (-b ± √(b^2 - 4ac)) / (2a)

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

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

Simplifying further:

y = (3 ± √(9 + 216)) / 2

y = (3 ± √225) / 2

y = (3 ± 15) / 2

Step 4: Solve for y using both the positive and negative square root values:

For the positive square root:
y = (3 + 15)/2
y = 18/2
y = 9

For the negative square root:
y = (3 - 15)/2
y = -12/2
y = -6

Therefore, the solutions to the equation y^2 - 3y = 54 are y = 9 and y = -6.