(x-5)2=3x2-x+14 решите уровнение

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To solve the equation, we need to first expand the left side of the equation:

(x-5)^2 = (x-5)(x-5)
(x-5)^2 = x^2 - 5x - 5x + 25
(x-5)^2 = x^2 - 10x + 25

Now the equation becomes:

x^2 - 10x + 25 = 3x^2 - x + 14

Next, simplify the equation by moving all terms to one side:

0 = 3x^2 - x + 14 - x^2 + 10x - 25
0 = 2x^2 + 9x - 11

Now we have a quadratic equation. To solve for x, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 2, b = 9, and c = -11. Plugging in these values:

x = (-9 ± √(9^2 - 42(-11))) / 2*2
x = (-9 ± √(81 + 88)) / 4
x = (-9 ± √169) / 4
x = (-9 ± 13) / 4

This gives us two possible solutions:

x = (4/4) = 1
x = (-22/4) = -5.5

Therefore, the solutions to the equation are x = 1 and x = -5.5.