$$Statement\ 1:\ 3x^2+8x+\frac{16}{3}=0$$
Multiply by 3 to make a standard quadratic equation
We have,
$$9x^2+24x+16=0$$
$$9x^2+12x+12x+16=0$$
$$\left(9x^2+12x\right)+\left(12x+16\right)=0$$
$$3x\left(3x+4\right)+4\left(3x+4\right)=0$$
$$\left(3x+4\right)\cdot\left(3x+4\right)=0$$
$$\sqrt{\left(3x+4\right)}=0$$
On squaring both sides, we have
$$3x+4=0$$
$$x=-\frac{4}{3}$$
Statement 1 is SUFFICIENT
$$Statement\ 2:\ 15x^2+\frac{80}{3}=-40x$$
$$15x^2+40x+\frac{80}{3}=0$$
Multiply by 3 to make a standard quadratic equation
We have,
$$45x^2+120x+80=0$$
Divide through by 5
$$9x^2+24x+16=0$$
This is similar to information in statement 1; hence, statement 2 is also SUFFICIENT.
Since each statement is SUFFICIENT alone, it validates option D as the correct answer.
