5/(2x) - 4/(x^{2}) = 7/(2x^{2})

First, set the equation equal to 0 by moving all the terms to one side of the equation. For simplicity, subtract 7/(2x^{2}) from both sides of the equation:

5/(2x) - 4/(x^{2}) - 7/(2x^{2}) = 0

Now we went to generate a least common denominator among all terms on the left hand side of the equation. Notice that 2x^{2} is the least common denominator here, so we want to manipulate all of the terms in a way such that they all have a denominator of 2x^{2}. To do this, multiply the numerator and the denominator of the first term by x and multiply the numerator and the denominator of the second term by 2:

5(x)/(2x)(x) - 4(2)/(x^{2})(2) - 7/(2x^{2}) = 0

5x/(2x^{2}) - 8/(2x^{2}) - 7/(2x^{2}) = 0

Since all the terms now share a common denominator, we can add their numerators:

(5x - 8 - 7)/(2x^{2}) = 0

(5x - 15)/(2x^{2}) = 0

After we cross-multiply, we arrive at the following:

5x - 15 = 0

Adding 15 to both sides of the equation we get the following:

5x = 15

Divide both sides of the equation by 5 to solve for x:

x = 3