For the first equation, we can simplify it to:
2x^2 + 1 = 0

Now, we can solve for x using the quadratic formula:
x = [-b ± √(b^2 - 4ac)] / 2a

In this case, a = 2, b = 0, and c = 1. Plugging in these values:
x = [0 ± √(0 - 4(2)(1))] / 2(2)
x = [0 ± √(-8)] / 4
x = ±√2i / 4
x = ±(√2i / 4)

So the solutions for the first equation are:
x = √2i / 4 or x = -√2i / 4

For the second equation, we can solve for x using the quadratic formula:
x = [-(-9) ± √((-9)^2 - 4(4)(7))] / 2(4)
x = [9 ± √(81 - 112)] / 8
x = [9 ± √(-31)] / 8
x = [9 ± i√31] / 8

So the solutions for the second equation are:
x = (9 + i√31) / 8 or x = (9 - i√31) / 8