Question

Find the roots of √7 x^2 -6x -13√7 = 0

Answer 1

$\sqrt{7} {x}^{2} - 6x - 13 \sqrt{7} = 0$

$\sqrt{7} {x}^{2} - 13x + 7x - 13 \sqrt{7} = 0$

$x( \sqrt{7} x - 13) + \sqrt{7} ( \sqrt{7} x - 13) = 0$

therefore

$(x + \sqrt{7} ) \times ( \sqrt{7} x - 13) = 0$

therefore

$x = - \sqrt{7} \: or \: 13 \div \sqrt{7}$