To solve the equation , first, isolate the square root by dividing both sides by 3, giving you . Next, square both sides to eliminate the square root: . Multiply the whole equation by 9 to clear the fraction: . Rearranging gives . Use the quadratic formula to find the values of .

Real-world applications of quadratic equations like this one can be found in various fields, such as engineering and physics, where understanding the shape of a trajectory or optimizing designs is crucial. Solving such equations often reveals important insights about positions, forces, or materials’ properties, making them not just theoretical exercises but practical tools for innovation.

A common mistake when dealing with equations involving square roots is to forget to check for extraneous solutions. After squaring both sides, there’s a risk of introducing solutions that don’t satisfy the original equation. So after solving , be sure to substitute the potential solutions back into the original equation to ensure they are valid!