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