How can I isolate x in y=6x-2x²

x = 3/2 ± √ (9/4 - 1/2 y)

Step-by-step explanation:

y = 6x - 2x²

First, factor out the leading coefficient:

y = - 2 (x² - 3x)

Complete the square.

y = - 2 (x² - 3x + 9/4 - 9/4)

y = - 2 (x² - 3x + 9/4) + 9/2

y = - 2 (x - 3/2) ² + 9/2

Solve for x.

-1/2 y = (x - 3/2) ² - 9/4

9/4 - 1/2 y = (x - 3/2) ²

±√ (9/4 - 1/2 y) = x - 3/2

x = 3/2 ± √ (9/4 - 1/2 y)