Solve the following by factorisation: $8 x^{2} - 22 x - 21 = 0$ .

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Solution

Step: Solve the given equation by factorisation
$\Rightarrow 8 x^{2} - 22 x - 21 = 0 \Rightarrow 8 x^{2} - 28 x + 6 x - 21 = 0 \Rightarrow 4 x (2 x - 7) + 3 (2 x - 7) = 0 \Rightarrow (4 x + 3) (2 x - 7) = 0 \Rightarrow 4 x + 3 = 0 o r 2 x - 7 = 0 \Rightarrow x = - \frac{3}{4} o r x = \frac{7}{2}$
Thus, the roots of the equation from factorisation are $- \frac{3}{4}$ and $\frac{7}{2}$ .

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