Final answer:
To solve the equation 5x = 6x² - 3 using the quadratic formula, rearrange the equation to be in the form ax² + bx + c = 0. Substitute the values into the quadratic formula and solve for x. The values of x are approximately 0.664 and -0.831.
Step-by-step explanation:
To solve the equation 5x = 6x2 - 3 using the quadratic formula, we can rearrange the equation to be in the form ax2 + bx + c = 0. In this case, a = 6, b = -5, and c = -3. The quadratic formula is:
x = (-b ± √(b2 - 4ac)) / (2a)
Substituting the values of a, b, and c into the formula, we get:
x = (-(-5) ± √((-5)2 - 4(6)(-3))) / (2(6))
x = (5 ± √(25 + 72)) / 12
x = (5 ± √97) / 12
Therefore, the values of x are approximately 0.664 and -0.831.