To solve this equation, let's first simplify the equation:

x^2 + 7x + 10 = sqrt(72)

Next, let's simplify the right side of the equation:

sqrt(72) = sqrt(36 2) = sqrt(36) sqrt(2) = 6 * sqrt(2)

Therefore, the equation becomes:

x^2 + 7x + 10 = 6√2

Next, let's move the terms to one side:

x^2 + 7x + 10 - 6√2 = 0

Now, we have a quadratic equation:

x^2 + 7x + (10 - 6√2) = 0

Now, we can solve this quadratic equation using the quadratic formula:

x = [-b ± sqrt(b^2 - 4ac)] / 2a

Where a = 1, b = 7, and c = 10 - 6√2

Plugging in the values:

x = [-7 ± sqrt(7^2 - 41(10-6√2))] / 2*1
x = [-7 ± sqrt(49 - 40 + 24√2)] / 2
x = [-7 ± sqrt(9 + 24√2)] / 2

Therefore, the solutions to the equation x^2 + 7x + 10 = 6√2 are:

x = (-7 + sqrt(9 + 24√2)) / 2
x = (-7 - sqrt(9 + 24√2)) / 2