# Solve the following quadratic equation 3x^2 + 5x + 2 = 0

Solve the following quadratic equation $$\displaystyle{3}{x}^{{2}}+{5}{x}+{2}={0}$$

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The quadratic formula used for quadratic equation $$\displaystyle{a}{x}^{{2}}+{b}{x}+{c}={0}$$ is,
$$\displaystyle{x}=-\frac{{{b}\pm\sqrt{{{b}^{{2}}-{4}{a}{c}}}}}{{{2}{a}}}$$
Apply the quadratic formula in $$\displaystyle{3}{x}^{{2}}+{5}{x}+{2}={0}$$ then
$$\displaystyle{x}=\frac{{-{5}\pm\sqrt{{{5}^{{2}}-{4}\times{3}\times{2}}}}}{{{2}\times{3}}}$$
$$\displaystyle{x}={\left(-{5}\pm\frac{\sqrt{{{25}-{24}}}}{{6}}\right)}$$
$$\displaystyle{x}=\frac{{-{5}\pm{1}}}{{6}}$$
$$\displaystyle{x}=-\frac{{2}}{{3}},-{1}$$