0,5у^3-0, 5у(у+1) (у-3) =7

To solve the equation:

0.5y^3 - 0.5y(y+1)(y-3) = 7

We can start by expanding the terms inside the parentheses:

0.5y^3 - 0.5y(y^2 - 2y - 3) = 7

Simplifying further:

0.5y^3 - 0.5y^3 + y^2 - y - 1.5y = 7

Combine like terms:

y^2 - 1.5y - 7 = 0

Now we have a quadratic equation. We can solve for y by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:

y = (-b ± sqrt(b^2 - 4ac)) / (2a)

In our case, a = 1, b = -1.5, and c = -7. Substituting these values into the quadratic formula:

y = (-(-1.5) ± sqrt((-1.5)^2 - 4(1)(-7))) / (2(1))

Simplifying:

y = (1.5 ± sqrt(2.25 + 28)) / 2

y = (1.5 ± sqrt(30.25)) / 2

y = (1.5 ± 5.5) / 2

This gives us two possible solutions:

y1 = (1.5 + 5.5) / 2 = 7 / 2 = 3.5

y2 = (1.5 - 5.5) / 2 = -4 / 2 = -2

So the solutions to the equation are y = 3.5 and y = -2.