# Using the quadratic formula solve xsquared=2/3x

Using the quadratic formula solve xsquared=2/3x

x^2 - 2x/3 = 0

x = [+2/3+/-sqrt(2/3^2 - 4(1)0)]/2

## To solve the equation x^2 = (2/3)x using the quadratic formula, we need to rearrange the equation to the form ax^2 + bx + c = 0.

In this case, we have x^2 - (2/3)x = 0, so a = 1, b = -2/3, and c = 0.

The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values from our equation:

x = (-(2/3) ± √((2/3)^2 - 4(1)(0))) / (2(1))

x = (-2/3 ± √(4/9 - 0)) / 2

Simplifying the expression:

x = (-2/3 ± √(4/9)) / 2

To simplify the square root, we take the square root of the numerator and denominator separately:

x = (-2/3 ± (2/3)) / 2

Now we have two options:

1. x = (-2/3 + 2/3) / 2

x = 0 / 2

x = 0

2. x = (-2/3 - 2/3) / 2

x = -4/3 / 2

x = -2/3

So the solutions to the equation x^2 = (2/3)x are x = 0 and x = -2/3.