Simplify the equation:

6x + 2 = 810

Subtract 2 from both sides:

6x = 808

Divide by 6:

x = 134

Now substitute x back into the original equation to find the value of the second term:

{3}^{134 + 2} + {3}^{134} = 810

{3}^{136} + {3}^{134} = 810

Solve for the values of the exponential terms:

{3}^{136} = 3^4 = 81

{3}^{134} = 3^2 = 9

81 + 9 = 90

Therefore, the solution to the equation is x = 134.