Question: Solve: $4 \sqrt{a -3} = \sqrt{5a +7}$

Solution:
Given,

$4 \sqrt{a -3} = \sqrt{5a +7}$

[ Squaring both sides ]

$or, (4 \sqrt{a -3})^2 = ( \sqrt{5a +7})^2$

$or, 16(a-3) = 5a +7$

$or, 16a - 48 = 5a +7$

$or, 16a -5a = 48+7$

$or, 11a = 55$

$\therefore a = 5$