Final answer:
To solve the equation 3x² + 3x - 90 = 0, use the quadratic formula to find the values of x. Plugging the values into the formula and simplifying, we get two possible solutions: x = 4 and x = -5.
Step-by-step explanation:
To solve the equation 3x² + 3x - 90 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± sqrt(b² - 4ac)) / 2a
In our equation, a = 3, b = 3, and c = -90. Plugging these values into the quadratic formula, we get:
x = (-3 ± sqrt(3² - 4(3)(-90))) / (2(3))
Simplifying the equation further, we have:
x = (-3 ± sqrt(729)) / 6
Taking the square root of 729, we get 27. So the equation becomes:
x = (-3 ± 27) / 6
Solving for x, we get two possible solutions:
x = (-3 + 27) / 6 = 24/6 = 4
x = (-3 - 27) / 6 = -30/6 = -5