Solve the equation. \[ \sqrt{5 x+70}-3=3 x-11 \]

Step 1 ：Isolate the square root on one side of the equation by adding 3 to both sides of the equation: \(\sqrt{5 x+70}=3 x-8\)

Step 2 ：Square both sides of the equation to eliminate the square root: \(5 x+70=(3 x-8)^2\)

Step 3 ：Solve the quadratic equation by setting it equal to zero and then using the quadratic formula: x = -1/9 and x = 6

Step 4 ：Check these solutions in the original equation because squaring both sides of an equation can sometimes introduce extraneous solutions: The solution x = -1/9 does not satisfy the original equation, but the solution x = 6 does

Step 5 ：Final Answer: The solution to the equation is \(\boxed{6}\)