The solution of this equation is x = 5 and x = 9.
<h3>What is the solution?</h3>
Let us recall that what we have here is a radical equation as follows;
√7x+1 - √x-5 = 6
When we isolate we have';
√7x+1 = √x-5+6
Taking the square of both sides;
(√7x+1)^2 = (√x-5+6)^2
Hence;
7x+1 = x-5+36+12√x-5
-12√x-5 = -7x-1+x-5+36
12√x-5 = 6x-30
Raising this equation to power 2
144x-720 = 36x^2-360x+900
When we rearrange we obtain;
36x2 - 504x + 1620 = 0
Hence;
x = 5 and x = 9
Learn more about radical equation:brainly.com/question/8606917
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