0,5у^3-0, 5у(у+1) (у-3) =7

To solve the given equation, we need to simplify and rearrange the terms. Let's start by expanding the equation:

0,5у^3 - 0,5у(у + 1)(у - 3) = 7

Expanding the expression (у + 1)(у - 3), we get:

0,5у^3 - 0,5у(у^2 - 2у - 3) = 7

Simplifying further, we distribute -0,5у into (у^2 - 2у - 3):

0,5у^3 - 0,5у * у^2 + 0,5у * 2у + 0,5у * 3 = 7

0,5у^3 - 0,5у^3 + у^2 - у - 1,5у = 7

Canceling out the common terms, we get:

у^2 - 2,5у = 7

Rearranging the terms, we obtain:

у^2 - 2,5у - 7 = 0

Now, we have a quadratic equation. To solve for у, we can use factoring, completing the square, or the quadratic formula. Let's solve it using the quadratic formula.

The quadratic formula is given by:

у = (-b ± √(b^2 - 4ac)) / 2a

In our equation, a = 1, b = -2.5, and c = -7. Substituting these values into the quadratic formula, we have:

у = (-(-2.5) ± √((-2.5)^2 - 4(1)(-7))) / (2 * 1)

Simplifying further:

у = (2.5 ± √(6.25 + 28))/2

у = (2.5 ± √34.25)/2

Finally, we have two possible solutions:

у = (2.5 + √34.25)/2 у = (2.5 - √34.25)/2

These are the values of у that satisfy the given equation.