Solve the the given equation: $\sqrt{3x^2+x+5} = x-3$ We have to find the number of solution for the given equation:
$$\sqrt{3x^2+x+5} = x-3.$$
There are two solution one is
By using graph we get one solution

By squaring both sides we get no solution

I want to know which solution is correct

Hint:
The given equation is equivalent to the system:
$$
\begin{cases}
3x^2+x+5=(x-3)^2\\
x-3\ge 0
\end{cases}
$$

Note that the system has no solutions because the roots of the second degree equations :
$$
x=\frac{-7\pm\sqrt{79}}{4}
$$
are less than $3$. 
And this is in accord with the fact that the graphs of the two functions
$$
y=\sqrt{3x^2+x+5} \qquad y=x-3
$$
have no common points (in your graph you  have the wrong function $x=3$).

