Question

8.0x=x^3+3.0x^2 solve for x

Answer 1

First of all, move all terms to the same side:

$x^3 + 3x^2 - 8 x = 0$

You can factor an x, which means that $x = 0$ is a solution:

$x(x^2+3x-8)$

This expression is further factorizable if the quadratic equation has any solution. Using the quadratic formula, we can find that they are

$x_{1,2} = -\dfrac{3 \pm \sqrt{41}}{2}$

So, we have

$x(x^2+3x+8) = 0 = \iff x = 0,\quad x =-\dfrac{3 + \sqrt{41}}{2} ,\quad x =-\dfrac{3 - \sqrt{41}}{2}$