How do you solve

1/2x^2 - x + 4 ?

There is no equal sign, nothing to solve.

if it's 1/(2x^2) - x + 4 = 0

Multiply across by 2x^2 to get
1 - 2x^3 + 8x^2 = 0
2x^3 - 8x^2 - 1 = 0

Which is a nasty enough cubic with only 1 root.

If the question is (1/2)x^2 - x + 4 = 0
use the -b formula which gives 2 complex roots: 1 + sqrt(7)i and 1 - sqrt(7)i.

Hope that helps

To solve the quadratic equation 1/2x^2 - x + 4, we can use the quadratic formula or factorization method. Let's solve it using the quadratic formula.

The quadratic formula states that for any quadratic equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

Now, let's apply this formula to our equation, 1/2x^2 - x + 4:

a = 1/2
b = -1
c = 4

Putting these values into the quadratic formula,
x = (-(-1) ± sqrt((-1)^2 - 4 * (1/2) * 4)) / (2 * (1/2))

Simplifying further:
x = (1 ± sqrt(1 - 8))/1
x = (1 ± sqrt(-7))/1

Since we have a negative value under the square root (√), the equation has no real solutions (no real values of x). Instead, it has complex solutions. The square root of -7 is an imaginary number.

Thus, the equation 1/2x^2 - x + 4 has no real solutions.