Question

Use the quadratic formula to solve 3x^2=5x

Answer 1

First of all, we have to set the equation in the form $p(x)=0$, where $p(x)$ is a quadratic polynomial. So, we have

$3x^2-5x=0$

Even though using the quadratic formula for such a simple case is a little bit overkill, it is surely doable: we have

$3x^2-5x=0 \iff ax^2+bx+c=0 \iff a=3,\quad b=-5,\quad c=0$

And the formula for solving is

$x_{1,2} = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

So, if we plug our values, we have

$x_{1,2} = \dfrac{5\pm\sqrt{25}}{6} = \dfrac{5\pm5}{6}$

And thus the solutions are

$x_1=0,\quad x_2 = \dfrac{10}{6}=\dfrac{5}{3}$