Find the roots of the given equation: $8 x^{2}-14 x-15=0$

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Find the roots of the given equation: $8 x^{2}-14 x-15=0$

$8 x^{2}-14 x-15=0$
$\Rightarrow 16 x^{2}-28 x-30=0 \quad$ (Multiplying both sides by 2) $\Rightarrow 16 x^{2}-28 x=30$
$\Rightarrow(4 x)^{2}-2 \times 4 x \times \frac{7}{2}+\left(\frac{7}{2}\right)^{2}=30+\left(\frac{7}{2}\right)^{2} \quad$ [Adding $\left(\frac{7}{2}\right)^{2}$ on both sides,
$\Rightarrow\left(4 x-\frac{7}{2}\right)^{2}=30+\frac{49}{4}=\frac{169}{4}=\left(\frac{13}{2}\right)^{2}$
$\Rightarrow 4 x-\frac{7}{2}=\pm \frac{13}{2} \quad$ (Taking square root on both sides)
$\Rightarrow 4 x-\frac{7}{2}=\frac{13}{2}$ or $4 x-\frac{7}{2}=\frac{13}{2}$
$\Rightarrow 4 x=\frac{13}{2}+\frac{7}{2}=\frac{20}{2}=10$ or $4 x=-\frac{13}{2}+\frac{7}{2}=-\frac{6}{2}=-3$
$\Rightarrow x=\frac{5}{2}$ or $x=-\frac{3}{4}$