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
Answer: x = 1/2, or x = -7/2
