MathJax 3

$\sqrt{x}$ $$\begin{aligned}3x^2-4x-5&=0\end{aligned}$$ Using the quadratic formula, $$x=\frac{-(-4)\pm\sqrt{(-4)^2-4(3)(-5)}}{2(3)}.$$ Simplify: $$\begin{aligned}x&=\frac{4\pm\sqrt{16+60}}{6} \&=\frac{4\pm\sqrt{76}}{6} \&=\frac{4\pm2\sqrt{19}}{6} \&=\frac{2\pm\sqrt{19}}{3}.\end{aligned}$$ Therefore, $$\boxed{x=\frac{2+\sqrt{19}}{3}\quad\text{or}\quad x=\frac{2-\sqrt{19}}{3}.}$$ WP QuickLatex $$\begin{aligned}3x^2+4x-5&=0\end{aligned}$$ Using the quadratic formula, $$x=\frac{-4\pm\sqrt{4^2-4(3)(-5)}}{2(3)}.$$ Simplify: $$\begin{aligned}x&=\frac{-4\pm\sqrt{16+60}}{6}\&=\frac{-4\pm\sqrt{76}}{6}\&=\frac{-4\pm2\sqrt{19}}{6}\&=\frac{-2\pm\sqrt{19}}{3}.\end{aligned}$$ Therefore, $$\boxed{x=\frac{-2+\sqrt{19}}{3}\quad\text{or}\quad x=\frac{-2-\sqrt{19}}{3}.}$$ Try again: $$3x^2+4x-5=0$$ Using the quadratic formula, $$x=\frac{-4\pm\sqrt{4^2-4(3)(-5)}}{2(3)}.$$ Simplify: \begin{align} x &=\frac{-4\pm\sqrt{16+60}}{6}\ &=\frac{-4\pm\sqrt{76}}{6}\ &=\frac{-4\pm2\sqrt{19}}{6}\ &=\frac{-2\pm\sqrt{19}}{3}. \end{align} Therefore, $$\boxed{x=\frac{-2+\sqrt{19}}{3}\quad\text{or}\quadx=\frac{-2-\sqrt{19}}{3}}$$