Step 1 :Given the quadratic equation \(2x^{2} + 3x - 7 = 0\), we can solve for \(x\) using the quadratic formula.
Step 2 :The quadratic formula is given by \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a\), \(b\), and \(c\) are coefficients of the quadratic equation \(ax^2 + bx + c = 0\).
Step 3 :In this case, \(a = 2\), \(b = 3\), and \(c = -7\).
Step 4 :Substitute these values into the quadratic formula to find the solutions for \(x\).
Step 5 :Calculate the discriminant \(D = b^2 - 4ac = 65\).
Step 6 :Solve for \(x\) to get \(x1 = 1.27\) and \(x2 = -2.77\).
Step 7 :The solutions to the equation are \(x = \boxed{1.27}\) and \(x = \boxed{-2.77}\).