Solve the Problem $3 x ^ { 2 } + 2 x - 5 = 0$

Solve the problem.
-Use Newton's method to estimate the solutions of the equation $3 x ^ { 2 } + 2 x - 5 = 0$ . Start with $x _ { 1 } = 0.5$ for the right-hand solution and with $x _ { 0 } = - 2$ for the solution on the left. Then, in each case find $x _ { 2 }$ .