To solve the equation, we will start by simplifying each square root expression:

√(36-126) = √(-90) = √(9 * -10) = 3i√10

√(x-6) = √(x-6)

√(4x-24) = √(4(x-6)) = 2√(x-6)

√(49x-343) = √(49(x-7)) = 7√(x-7)

Now, let's substitute these values back into the equation:

3i√10 - √(x-6) + 7/2 * 2√(x-6) = 3/7 * 7√(x-7)

Simplifying further:

3i√10 - √(x-6) + 7√(x-6) = 3√(x-7)

Combining like terms:

(7√(x-6) - √(x-6)) + 3i√10 = 3√(x-7)

Simplifying:

6√(x-6) + 3i√10 = 3√(x-7)

Now, let's isolate the square root terms on one side and the constant terms on the other side:

6√(x-6) - 3√(x-7) = -3i√10

Factoring out the common square root term:

3√(x-6)(2 - √(x-7)) = -3i√10

Dividing both sides by -3i√10:

√(x-6)(2 - √(x-7)) = i

Squaring both sides to eliminate the square root:

(x-6)(2 - √(x-7))^2 = -1

Expanding the square:

(x-6)(4 - 4√(x-7) + x-7) = -1

Simplifying:

(x-6)(x - 3 - 4√(x-7)) = -1

Expanding the product:

x^2 - 3x - 4x√(x-7) - 6x + 18 + 24√(x-7) = -1

Combining like terms:

x^2 - 9x + 18 + 20√(x-7) = -1

Moving all terms to one side:

x^2 - 9x + 19 + 20√(x-7) = 0

This is the simplified form of the equation. Unfortunately, it cannot be solved algebraically. You would need to use numerical methods or approximation techniques to find an approximate solution.