for the function y=2x^2+5X-k one of the zeros is at x=-4. Determine the other x intercept.Full thorough explanation of solution and steps

We have y= 2x^2 + 5x - k which is a quadratic equation and
we are given that one of the roots is at x = -4.

The roots
of 2x^2 + 5x - k lie at :

x = -5/4 + sqrt (25 + 8k)/4 and x
= -5/4 - sqrt (25 + 8k)/4

As one of the roots is
-4

-5/4 - sqrt (25 + 8k)/4 =
-4

=> -5 - sqrt(25 + 8k) =
-16

=> sqrt(25 + 8k) =
11

=> (25 + 8k) =
121

=> (25 + 8k) =
121

=> 8k =
96

=> k = 12

The other
root is at x = -5/4 + sqrt (25 + 8k)/4

=> x = -5/4 +
sqrt (25 + 96)/4

=> -5/4 +
11/4

=> 6/4

=>
3/2

As x = 3/2 is the other root, this is also the point
where the other x-intercept lies.

The other
x-intercept of y = 2x^2 + 5x - k is (3/2, 0).