# Solve the following quadratic equation 6x^2-x-15=0

Question
Solve the following quadratic equation $$\displaystyle{6}{x}^{{2}}-{x}-{15}={0}$$

2020-10-26
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 $$\displaystyle{6}{x}^{{2}}-{x}-{15}={0}$$ then
$$\displaystyle{x}=\frac{{-{1}{\left(-{1}\right)}\pm\sqrt{{{\left(-{1}\right)}^{{2}}-{4}\times{6}\times{\left(-{15}\right)}}}}}{{{2}\times{6}}}$$
$$\displaystyle{x}=\frac{{{1}\pm\sqrt{{{1}+{160}}}}}{{12}}$$
$$\displaystyle{x}=\frac{{{1}\pm\sqrt{{{361}}}}}{{6}}$$
$$\displaystyle{x}=\frac{{{1}+{19}}}{{6}}$$
$$\displaystyle{x}=\frac{{5}}{{3}},\frac{{3}}{{2}}$$

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