$4 b^{2}+8 b+7=4$

Step 1 ：The given equation is a quadratic equation in the form of \(ax^2 + bx + c = 0\). We can solve this equation using the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).

Step 2 ：Identify the coefficients in the equation: \(a = 4\), \(b = 8\), and \(c = 3\).

Step 3 ：Calculate the discriminant (D) using the formula \(D = b^2 - 4ac\). Substituting the values, we get \(D = 16\).

Step 4 ：Substitute the values of a, b, and D into the quadratic formula to find the solutions. The solutions are \(sol1 = -1.5\) and \(sol2 = -0.5\).

Step 5 ：The solutions to the equation \(4 b^{2}+8 b+7=4\) are \(\boxed{-1.5}\) and \(\boxed{-0.5}\).