To solve this equation, we need to first simplify the expression on the left side of the equation:

-3/4 + 2x ÷ 3/2

First, let's simplify the division by multiplying by the reciprocal of 3/2:

-3/4 + 2x * 2/3

Now, we can simplify the expression further:

-3/4 + 4x/3

To combine the fractions, we need a common denominator. The common denominator is 12:

-9/12 + 16x/12

Now, we can combine the fractions:

(-9 + 16x) / 12

Now, we can set this expression equal to -1/4:

(-9 + 16x) / 12 = -1/4

To solve for x, we can cross multiply:

-9 + 16x = -3

Now, we can solve for x:

16x = -3 + 9
16x = 6
x = 6/16
x = 3/8

Therefore, the solution to the equation is x = 3/8.