<s>[INST] 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
 [/INST] we have $$\sqrt{3x^2+x+5}=x-3$$ it must be $$x\geq 3$$ and after squaring we get
$$3x^2+x+5=x^2-6x+9$$ this is equivalent to $$2x^2+7x-4=0$$ solving this quadratic equation we obtain
$$x_{1,2}=-\frac{7}{4}\pm\sqrt{\frac{49}{16}+\frac{32}{16}}$$
Can you finish this?
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