One of the roots of the equation 3x ^ 2 + bx + 4 = 0 is 1, and the other root is the same as the root

One of the roots of the equation 3x ^ 2 + bx + 4 = 0 is 1, and the other root is the same as the root of the equation 2x-3 = m. Find m.

We have the equation: 3x ^ 2 + bx + 4 = 0; (one)
1) By Vieta’s theorem, the product of the roots of the quadratic equation a x ^ 2 + b x + c = 0 is equal to c / a;
2) The root of the equation is 2x – 3 = m; x1 = (m + 3) / 2 is one of the roots of equation (1), the second root is 1.
c / a = 4/3;
Then:
x1 x2 = 1 (m + 3) / 2 = c / a = 4/3;
(m + 3) / 2 = 4/3;
m = 8/3 – 3 = -1/3;
Answer: m = -1/3.