Answer
$x=\dfrac{1\pm \sqrt{13}}{4}$
Work Step by Step
Using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ or the Quadratic Formula, the solutions of the given quadratic equation, $
4x^2-2x-3=0
,$ are
\begin{array}{l}\require{cancel}
x=\dfrac{-(-2)\pm\sqrt{(-2)^2-4(4)(-3)}}{2(4)}
\\\\
x=\dfrac{2\pm\sqrt{4+48}}{8}
\\\\
x=\dfrac{2\pm\sqrt{52}}{8}
\\\\
x=\dfrac{2\pm\sqrt{4\cdot13}}{8}
\\\\
x=\dfrac{2\pm\sqrt{(2)^2\cdot13}}{8}
\\\\
x=\dfrac{2\pm2\sqrt{13}}{8}
\\\\
x=\dfrac{2(1\pm \sqrt{13})}{8}
\\\\
x=\dfrac{\cancel{2}(1\pm \sqrt{13})}{\cancel{2}(4)}
\\\\
x=\dfrac{1\pm \sqrt{13}}{4}
.\end{array}
