Solve for $x$ : $6 x^{2} + 40 = 31 x$

\frac{3}{8}, \frac{2}{5}

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\frac{3}{8}, \frac{3}{2}

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0, \frac{8}{3}

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\frac{8}{3}, \frac{5}{2}

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Solution

The correct option is D $\frac{8}{3}, \frac{5}{2}$
Here the quadratic equation is ,
$6 x^{2} + 40 = 31 x$
$\Rightarrow 6 x^{2} - 31 x + 40 = 0$
$\Rightarrow 6 x^{2} - 16 x - 15 x + 40 x = 0$
$\Rightarrow 2 x (3 x - 8) - 5 (3 x - 8)$
$\Rightarrow (3 x - 8) (2 x - 5)$
$\Rightarrow 3 x - 8 = 0$
$\Rightarrow 3 x = 8$
$\Rightarrow x = \frac{8}{3}$ or $\Rightarrow 2 x - 5 = 0$
$\Rightarrow 2 x = 5$
$\Rightarrow x = \frac{5}{2}$

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