X^2+3x=7/4
solve the equation by completing the square

Note that
(x + a)^2 = x^2 + 2ax + a^2, so that x^2 + 2ax = (x + a)^2 - a^2

We want to solve
x^2 + 3x = 7/4

By setting a = 3/2, we obtain
x^2 + 3x = (x + 3/2)^2 - (3/2)^2

Therefore the given equation may be written as
(x + 3/2)^2 - (3/2)^2 = 7/4
(x + 3/2)^2 - 9/4 = 7/4
(x + 3/2)^2 = 7/4 + 9/4 = 16/4
 (x + 3/2)^2 = 4

Take square root of each side.
x + 3/2 = +/- 2

Therefore
x = +2 - 3/2 = 1/2
or 
x = -2 - 3/2 = -7/2

 x = 1/2, or x = -7/2