To solve the equation 5x^2 - 15 = -6x using the quadratic formula, we need to rewrite the equation in the form ax^2 + bx + c = 0. Here's the step-by-step solution:
Step 1: Rewrite the equation in standard form:
5x^2 + 6x - 15 = 0
Step 2: Identify the coefficients:
a = 5
b = 6
c = -15
Step 3: Apply the quadratic formula:
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values, we have:
x = (-6 ± √(6^2 - 4 * 5 * -15)) / (2 * 5)
x = (-6 ± √(36 + 300)) / 10
x = (-6 ± √336) / 10
x = (-6 ± 18.33) / 10
Step 4: Simplify:
x = (-6 + 18.33) / 10 or x = (-6 - 18.33) / 10
x = 12.33 / 10 or x = -24.33 / 10
x = 1.233 or x = -2.433
Therefore, the solutions to the equation 5x^2 - 15 = -6x are x = 1.233 and x = -2.433.