# How do you solve #y = 3x^2 − 2x − 5 #?

Thus,

I applied polynomial distribution and collection rules.

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To solve the equation y = 3x^2 - 2x - 5, you can use the quadratic formula, which states that for any quadratic equation in the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a = 3, b = -2, and c = -5. Substituting these values into the quadratic formula:

x = (-(-2) ± √((-2)^2 - 4(3)(-5))) / (2*3)

Simplify inside the square root:

x = (2 ± √(4 + 60)) / 6

x = (2 ± √64) / 6

x = (2 ± 8) / 6

This yields two solutions:

x₁ = (2 + 8) / 6 = 10 / 6 = 5/3

x₂ = (2 - 8) / 6 = -6 / 6 = -1

So, the solutions for the equation y = 3x^2 - 2x - 5 are x = 5/3 and x = -1.

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