Final answer:
To solve the given quadratic equation 2x^2-3x-9=0, we can use the quadratic formula. The solutions for x are x = 3 and x = -1.5.
Step-by-step explanation:
To solve the equation 2x^2-3x-9=0, we can use the quadratic formula.
Given an equation in the form ax^2+bx+c=0, the quadratic formula gives us the solutions for x:
x = (-b ± √(b^2-4ac))/(2a)
In this case, a = 2, b = -3, and c = -9. Plugging these values into the quadratic formula, we get:
x = (-(-3) ± √((-3)^2-4(2)(-9)))/(2(2))
Simplifying further, we have:
x = (3 ± √(9+72))/(4)
x = (3 ± √(81))/(4)
x = (3 ± 9)/(4)
Therefore, the solutions for x are:
x = (3 + 9)/(4) = 3
x = (3 - 9)/(4) = -1.5