To solve the equation x^2 + 9x + 20 = 2√(3x + 10), we can start by isolating the square root term on one side of the equation.

Subtracting 2√(3x + 10) from both sides, we get:

x^2 + 9x + 20 - 2√(3x + 10) = 0

Next, we can square both sides of the equation to eliminate the square root:

(x^2 + 9x + 20 - 2√(3x + 10))^2 = 0

Expanding the squared term, we have:

x^4 + 18x^3 + 101x^2 + 180x + 400 - 4(3x + 10)√(3x + 10) = 0

Simplifying further, we get:

x^4 + 18x^3 + 101x^2 + 180x + 400 - 12x√(3x + 10) - 40√(3x + 10) = 0

Now, we can collect like terms and isolate the square root term:

x^4 + 18x^3 + 101x^2 + (180 - 12√(3x + 10))x + (400 - 40√(3x + 10)) = 0

At this point, it is difficult to solve for x algebraically. You may need to use numerical methods or approximation techniques to find the solutions to this equation.