blank/5 - 1/2 = 3/blank

To find the value of blank, let's solve the equation step by step:

blank/5 - 1/2 = 3/blank

To get rid of denominators, let's multiply through by the LCD (Least Common Denominator) which is 10:

10 * (blank/5) - 10 * (1/2) = 10 * (3/blank)

2(blank) - 5 = 30/blank

Multiplying both sides by blank to eliminate the fraction:

2(blank) * blank - 5 * blank = 30

2(blank^2) - 5(blank) = 30

2blank^2 - 5blank - 30 = 0

Now, we have a quadratic equation. Let's solve it by factoring:

(2blank + 3)(blank - 10) = 0

Setting each factor equal to zero:

2blank + 3 = 0 or blank - 10 = 0

For 2blank + 3 = 0:
2blank = -3
blank = -3/2

For blank - 10 = 0:
blank = 10

So, the possible solutions for blank are -3/2 or 10.