Final answer:
The question involves solving an equation with square roots to find valid solutions. The provided information seems unrelated as it discusses the quadratic formula and operations with roots, rather than directly solving the presented equation. The correct approach requires isolating and squaring both sides to eventually form and solve a quadratic equation.
Step-by-step explanation:
The student's question involves checking which values are a solution to the equation √(2x+3) - √(x+1) = 1. To solve this, we first need to isolate one of the square roots and then square both sides of the equation to remove the square root. Next, we will simplify and solve the resulting quadratic equation.
However, the information provided does not directly relate to the student's question as it discusses the quadratic formula, equilibrium problems, and operations with roots in general contexts rather than solving the specific square root equation given by the student. To answer the question, we need to plug each option (a, b, c, d) for x into the equation and check which ones satisfy it. It seems there is confusion in the given information.
If the student's actual problem was a quadratic equation in the form ax²+bx+c = 0, the quadratic formula would be used, which is −b ± √(b² - 4ac) / (2a). The solutions that this formula provides are the values of x that make the original quadratic equation true.