Question

how to solve x2=2 (5x-6)

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Answer 1

Solution:

${x}^{2} = 2(5x - 6)$

${x}^{2} = 10x - 12$

${x}^{2} - 10x + 12 = 0$

by shridharacharya formula

$x = \frac{( - 10) + \sqrt{( { - 10) } ^{2} - 4 \times 1 \times 12} }{2 \times 1} \: \: and \: \: x = \frac{( - 10) - \sqrt{( { - 10)}^{2} - 4 \times 1 \times 12 } }{2 \times 1}$

$x = \frac{10 + \sqrt{100 - 48} }{2} \: \: and \: x = \frac{10 - \sqrt{100 - 48} }{2}$

$x = \frac{10 + \sqrt{52} }{2} \: \: and \: x = \frac{10 - \sqrt{52} }{2}$

$x = \frac{10 + 2 \sqrt{13} }{2} \: \: and \: x = \frac{10 - 2 \sqrt{13} }{2}$

$x = 5 + \sqrt{2} \: \: \: and \: x = 5 - \sqrt{2}$

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