Evaluate :
${3 x}^{2} = 2 x + 8$

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Solution

$3 x^{2} = 2 x + 8$
$\Rightarrow 3 x^{2} - 2 x - 8 = 0$
$\Rightarrow 3 x^{2} - 6 x + 4 x - 8 = 0$
[Middle term splitting]
$\Rightarrow 3 x (x - 2) + 4 (x - 2) = 0$
$\Rightarrow (3 x + 4) (x - 2) = 0$
$x = 2$ or $x = - \frac{4}{3}$ .

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