Solve the Problem $2 x - 4 x ^ { 2 } + 3 = 0$

Essay

Solve the problem.
-Use Newton's method to estimate the solutions of the equation $2 x - 4 x ^ { 2 } + 3 = 0$ . Start with $x _ { 1 } = 1.5$ for the right-hand solution and with $x _ { 0 } = - 1$ for the solution on the left. Then, in each case find $x _ { 2 }$ .