(-9x + 5)^(1/2) = (4x + 3)^(1/2)
-9x + 5 = +- (4x + 3)
Note: The +- is because (4x+3)^(1/2) can be 4x + 3 and -4x - 3. Also because (-9x+5)^(1/2) can be -9x + 5 and 9x - 5.
-9x + 5 = 4x + 3 and -9x + 5 = -4x - 3
-13x = -2 and -5x = -8
x = 2/13 and x = 5/8