To solve the equation, let's simplify the square roots first:

√(53) = √15 = √(35) = √3 * √5 = √3√5

√(103) = √30 = √(103) = √10√3

Now the equation becomes:

√3√5x + √10√3x - 10 = 84

Simplify further:

√15x + √30x - 10 = 84

Combine like terms:

(√15 + √30)x - 10 = 84

Now isolate the x term:

(√15 + √30)x = 94

x = 94 / (√15 + √30)

This is the simplified form of the solution for the equation.