To find the value inside the square root, we start by calculating the discriminant:
Discriminant = b^2 - 4ac
In this case, a=2, b=7, and c=-15:
Discriminant = 7^2 - 4(2)(-15)
Discriminant = 49 + 120
Discriminant = 169
Now we substitute this value back into the quadratic formula:
x = (-7 ± √169) / 4
x = (-7 ± 13) / 4
Therefore, the possible solutions are:
x = (-7 + 13) / 4 = 6 / 4 = 1.5
x = (-7 - 13) / 4 = -20 / 4 = -5