0,5у^3-0, 5у(у+1) (у-3) =7

To solve the equation 0.5у^3 - 0.5у(у + 1)(у - 3) = 7, we can begin by expanding the equation and collecting like terms.

First, let's expand the terms inside the parentheses:

0.5у^3 - 0.5у(у + 1)(у - 3) = 7 0.5у^3 - 0.5у(у^2 - 3у + у - 3) = 7 0.5у^3 - 0.5у(у^2 - 2у - 3) = 7 0.5у^3 - 0.5у^3 + у^2 - у - 1.5у + 1.5 = 7 у^2 - 2.5у + 1.5 = 7

Now, let's bring all the terms to one side to set the equation equal to zero:

у^2 - 2.5у + 1.5 - 7 = 0 у^2 - 2.5у - 5.5 = 0

Now we have a quadratic equation in the form of ay^2 + by + c = 0, where a = 1, b = -2.5, and c = -5.5.

To solve this equation, we can use the quadratic formula:

y = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values into the quadratic formula, we get:

y = (-(-2.5) ± √((-2.5)^2 - 4(1)(-5.5))) / (2(1)) y = (2.5 ± √(6.25 + 22)) / 2 y = (2.5 ± √(28.25)) / 2 y = (2.5 ± √(28.25)) / 2 y = (2.5 ± 5.318) / 2

Now we can solve for y:

y = (2.5 + 5.318) / 2 ≈ 3.409 y = (2.5 - 5.318) / 2 ≈ -1.909

Therefore, the solutions to the given equation are y = 3.409 and y = -1.909.