4.2 Quadratic equations and inequations — MATHS STD 11 Science — Question

Squaring both the sides, we get

$3 x^{2}+x+5=(x-3)^{2}$

$\Rightarrow 3 x^{2}+x+5=x^{2}+9-6 x$

$\Rightarrow 2 x^{2}+7 x-4=0$

$\Rightarrow 2 x^{2}+8 x-x-4=0$

$\Rightarrow 2 x(x+4)-1(x+4)=0$

$\Rightarrow x=\frac{1}{2}$ or $x=-4$

For $x=\frac{1}{2}$ and $x=-4$

$L.H.S.$ $\neq$ $R.H.S.$ of equation, $\sqrt{3 x^{2}+x+5}$ $=x-3$

Also, for every $x \in R, \mathrm{LHS} \neq \mathrm{RHS}$ of the given equation. 

$\therefore $ Given equation has no solution.