find the roots of the equation 4x²-4x+17=3x²-10-17​

Sure, let's solve the equation step by step.

First, let's simplify the equation by combining like terms:

4x² - 4x + 17 = 3x² - 10 - 17

This simplifies to:

4x² - 3x² - 4x + 27 = 0

Which further simplifies to:

x² - 4x + 27 = 0

Now, let's use the quadratic formula to find the roots of the equation. The quadratic formula is:

x = [-b ± sqrt(b² - 4ac)] / 2a

In this equation, a = 1, b = -4, and c = 27. Plugging these values into the quadratic formula gives:

x = [4 ± sqrt((-4)² - 4127)] / 2*1 x = [4 ± sqrt(16 - 108)] / 2

Since the value under the square root (the discriminant) is negative (16 - 108 = -92), there are no real roots for this equation. The roots are complex/imaginary.