To solve this equation, you will need to isolate the variable h on one side of the equation. To do this, you can start by adding 2 and y to both sides of the equation to get rid of the constants on the right side:
√3h² - 2 - y = 0
√3h² - 2 + 2 + y = 0 + 2 + y
√3h² = 2 + y
Next, you can square both sides of the equation to eliminate the square root on the left side:
(√3h²)² = (2 + y)²
3h² = 4 + 4y + y²
Then, you can rearrange the terms on the right side to get the equation in standard form:
3h² = 4 + 4y + y²
3h² = (4 + y)(1 + y)
Finally, you can divide both sides of the equation by 3 to isolate the variable h:
h² = (4 + y)/3
Since y is given as 5, you can substitute this value into the equation to find the value of h:
h² = (4 + 5)/3
h² = 9/3
h = √(9/3)
Since h is less than 0, the value of h must be negative.
Therefore, the value of h is -√(9/3).