Determine the roots of the given equation.: $y=6 x^{2}+6 x-7$

Step 1 ：Given the quadratic equation: \(y=6 x^{2}+6 x-7\)

Step 2 ：Set the equation equal to zero to find the roots: \(6 x^{2}+6 x-7 = 0\)

Step 3 ：Identify the coefficients for the quadratic formula. Here, \(a = 6\), \(b = 6\), and \(c = -7\)

Step 4 ：Calculate the discriminant \(D\) using the formula \(D = b^{2} - 4ac\). Substituting the values, we get \(D = 204\)

Step 5 ：Use the quadratic formula to find the roots: \(x = \frac{-b \pm \sqrt{D}}{2a}\)

Step 6 ：Substitute the values into the formula to get the roots: \(x1 = -1.6902380714238083\) and \(x2 = 0.6902380714238084\)

Step 7 ：Final Answer: The roots of the equation \(y=6 x^{2}+6 x-7\) are \(\boxed{-1.69}\) and \(\boxed{0.69}\)