Question

Solve the following equation using the general formula:
$3x^2+5\sqrt{2}x+2=0$

Answer 1

$3x^2+5\sqrt{2}x+2=0$

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{-5\sqrt{2}\pm \sqrt{(5\sqrt{2}{)}^2-4\times 2\times 3}}{2\times 3}$

$x=\frac{-5\sqrt{2}\pm \sqrt{50-24}}{2\sqrt{3}}=\frac{-5\sqrt{2}\pm \sqrt{26}}{2\sqrt{3}}$

$x=\frac{(-5\pm \sqrt{13})\sqrt{2}}{2\sqrt{3}}$

$\Rightarrow x=\frac{-5\pm \sqrt{13}}{\sqrt{6}}$

$\Rightarrow x=\frac{-5\pm \sqrt{13}}{\sqrt{6}}$

$\frac{-5-\sqrt{13}}{\sqrt{6}}$.