Solve \[ 162 x^{2}-252 x+98=0 \]

Step 1 ：Given the quadratic equation \(162 x^{2}-252 x+98=0\)

Step 2 ：This is a quadratic equation of the form \(ax^2 + bx + c = 0\). The solutions to this equation can be found using the quadratic formula, which is given by: \(x = [-b ± sqrt(b^2 - 4ac)] / (2a)\)

Step 3 ：In this case, \(a = 162\), \(b = -252\), and \(c = 98\). We can substitute these values into the quadratic formula to find the solutions.

Step 4 ：Calculate the discriminant \(D = b^2 - 4ac = 0\)

Step 5 ：Since the discriminant \(D = 0\), the square root term disappears and the solutions are simply \(-b / (2a)\).

Step 6 ：Substitute \(a\) and \(b\) into the equation, we get \(x = 0.7777777777777778\)

Step 7 ：Final Answer: The solution to the equation \(162 x^{2}-252 x+98=0\) is \(\boxed{0.7777777777777778}\)