Given the equation:
$$49 x^{3} + 14 x^{2} + x = 0$$
transform
Take common factor x from the equation
we get:
$$x \left(49 x^{2} + 14 x + 1\right) = 0$$
then:
$$x_{1} = 0$$
and also
we get the equation
$$49 x^{2} + 14 x + 1 = 0$$
This equation is of the form
a*x^2 + b*x + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{2} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{3} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 49$$
$$b = 14$$
$$c = 1$$
, then
D = b^2 - 4 * a * c =
(14)^2 - 4 * (49) * (1) = 0
Because D = 0, then the equation has one root.
x = -b/2a = -14/2/(49)
$$x_{2} = - \frac{1}{7}$$
The final answer for (49*x^3 + 14*x^2 + x) + 0 = 0:
$$x_{1} = 0$$
$$x_{2} = - \frac{1}{7}$$