Answer
No real solution
Work Step by Step
Squaring both sides, the given expression is equivalent to
$$
4x^2=x-3
.$$
Using the properties of equality, the equation above is equivalent to
$$\begin{aligned}
4x^2-x+3&=0
.\end{aligned}$$
Using $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ or the Quadratic Formula, with $a=4$, $b=-1$, and $c=3$, then
$$
x=\frac{-(-1)\pm\sqrt{(-1)^2-4(4)(3)}}{2(4)}=\frac{1\pm\sqrt{-47}}{8}
.$$
Since $\sqrt{-47}$ is not a real number, it means the given equation has no real solution.
