What are the solutions of 8x² = 6 + 22x?

Solution:

It is given that

8x² = 6 + 22x

We can write it as

8x² - 22x - 6 = 0

The formula to find the solution of a quadratic equation is

x = [-b ± √b² - 4ac] / 2a

We know that

a = 8

b = -22

c = -6

Substituting these values

x = [-(-22) ± √(-22)² - 4 × 8 × -6] / (2 × 8)

By further calculation

x = [22 ± √484 + 192] / 16

x = [22 ± √676] / 16

So we get

x = [22 ± 26] / 16

Here

x = (22 + 26) / 16 = 3

x = (22 - 26) / 16 = -1/4.

Therefore, the solutions are x = 3 or -1/4.

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What are the solutions of 8x² = 6 + 22x?

Summary:

The solutions of 8x² = 6 + 22x are x = 3 or -1/4. We have quadratic formula to determine the required values.