Solve the inequality. \[ 49 x^{2}+36<84 x \]

Step 1 ：Rearrange the inequality to a standard quadratic inequality form by subtracting 84x from both sides: \(49x^2 - 84x + 36 < 0\)

Step 2 ：Factor the quadratic expression by finding two numbers that multiply to 1764 and add to -84. These numbers are -42 and -42. So, the inequality can be written as: \((7x - 6)^2 < 0\)

Step 3 ：The square of a real number is always non-negative (greater than or equal to zero). Therefore, the only way for \((7x - 6)^2\) to be less than zero is if \(7x - 6 = 0\)

Step 4 ：Solve for x: \(7x - 6 = 0\) gives \(x = \frac{6}{7}\)

Step 5 ：However, this is the point where the inequality equals zero, not where it is less than zero. Since a square of a real number cannot be negative, there are no solutions to the inequality

Step 6 ：\(\boxed{\text{The solution to the inequality } 49x^2 - 84x + 36 < 0 \text{ is the empty set}}\)