To solve the equation, we can start by simplifying the square roots:

√(2+x) + √(4x^2-6x-10) = 0

Next, we can isolate one of the square roots by subtracting √(4x^2-6x-10) from both sides:

√(2+x) = -√(4x^2-6x-10)

Now, square both sides of the equation to eliminate the square roots:

(√(2+x))^2 = (-√(4x^2-6x-10))^2

2+x = 4x^2-6x-10

Rearrange the equation to form a quadratic equation:

4x^2 - 7x - 12 = 0

Now, we can solve this quadratic equation by factoring or using the quadratic formula. Let's use factoring:

(4x + 3)(x - 4) = 0

Setting each factor equal to zero:

4x + 3 = 0 or x - 4 = 0

Solving for x in each equation:

4x = -3 or x = 4

Dividing both sides of the first equation by 4:

x = -3/4

Therefore, the solutions to the equation are x = -3/4 and x = 4.