The quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / 2a
In this equation, a = 2, b = 7, and c = -15.
Substituting these values into the formula, we get:
x = (-7 ± √(7^2 - 4(2)(-15))) / (2)(2)
Simplifying inside the square root:
x = (-7 ± √(169)) / 4
x = (-7 ± 13) / 4
This gives us two possible solutions:
x = (-7 + 13) / 4 = 3/2
x = (-7 - 13) / 4 = -5/2
Therefore, the solutions to the quadratic equation 2x^2+7x-15=0 are x=3/2 and x=-5/2.