Using the quadratic formula to solve 5x = 6x² - 3, what are the values of x?

Solution:

5x = 6x² – 3 [Given]

On arranging the terms, we get

6x² - 5x - 3 = 0

The standard form of a quadratic equation ax² + bx + c = 0 is written as

x = [−b ± √(b² - 4ac)] / 2a

Comparing it with the given equation

a = 6

b = - 5

c = - 3

Substituting the values in the standard form

x = [-(-5) ± √{(-5)² − 4 × 6 × (-3)}] / (2 × 6)

x = [5 ± √97] / 12

Therefore, the values of x are (5 + √97)/12 and (5 - √97)/12.

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Using the quadratic formula to solve 5x = 6x² - 3, what are the values of x?

Summary:

Using the quadratic formula to solve 5x = 6x² - 3, the values of x are (5 + √97)/12 and (5 - √97)/12.