CAT 2019 Shift 1 Paper

case I : $\mathit{x}=0$.
Clearly, $\mathit{x}=0$ satisfy the equation.
case II : $\mathit{x}>0$
$\left|\mathit{x}\right|\left(6{\mathit{x}}^2+1\right)=5{\mathit{x}}^2$
$\Rightarrow \mathit{x}\left(6{\mathit{x}}^2+1\right)=5{\mathit{x}}^2$
$\Rightarrow 6{\mathit{x}}^2+1-5\mathit{x}=0$
On solving the quadratic equation, we get $\mathit{x}=\frac{1}{2},\frac{1}{3}$ (both valid)
Case III:
$\left|\mathit{x}\right|\left(6{\mathit{x}}^2+1\right)=5{\mathit{x}}^2$
$\Rightarrow -\mathit{x}\left(6{\mathit{x}}^2+1\right)=5{\mathit{x}}^2$
$\Rightarrow 6{\mathit{x}}^2+5\mathit{x}+1=0$
On solving the quadratic equation, we get $\mathit{x}=\frac{-1}{2},\frac{-1}{3}$ (both valid)
Hence there are 5 solutions.