Solve the following equation √x-1 + √5x+1 =2√x+6
Assuming the usual carelessness with parentheses, I'll go with
√(x-1) + √(5x+1) = 2√(x+6)
(x-1) + 2√((x-1)(5x+1)) + (5x+1) = 4(x+6)
x-12 = √((x-1)(5x+1))
(x-12)^2 = (x-1)(5x+1)
x^2-24x+144 = 5x^2-4x-1
4x^2+20x-145 = 0
...
Be sure to check your final answers in the original equation.