\( 1<\left\lvert\, \begin{array}{l}\text { Solve. Write the answer in standard form. } \\ 6 x^{2}+1=4 \mathrm{x}^{2}\end{array}\right. \)

First, let's rearrange the equation \(6x^2 + 1 = 4x^2\) by moving all terms to one side. Subtract \(4x^2\) from both sides to get: \[ 6x^2 - 4x^2 + 1 = 0 \] Which simplifies to: \[ 2x^2 + 1 = 0 \] Now, we'll isolate \(x^2\): \[ 2x^2 = -1 \] Dividing by 2 gives: \[ x^2 = -\frac{1}{2} \] Taking the square root of both sides leads us to: \[ x = \pm i \frac{1}{\sqrt{2}} \] In standard form, this can be rewritten as: \[ x = \pm \frac{i\sqrt{2}}{2} \] And there you have it! The solutions to the equation in standard form are: \[ x = \frac{i\sqrt{2}}{2} \quad \text{and} \quad x = -\frac{i\sqrt{2}}{2} \]