Answer
$x=0, x=\frac{-5 - 10\sqrt 2}{7}, x=\frac{-5 +10\sqrt 2}{7}$
Work Step by Step
Use factoring. $$
\begin{gathered}
1.75 x^3+2.5 x^2=6.25 x \\
1.75 x^3+2.5 x^2-6.25 x=0 \\
100\left(1.75 x^3+2.5 x^2-6.25 x\right)=0 \\
175 x^3+250 x^2-625 x=0 \\
25 x\left(7 x^2+10 x^2-25\right)=0.
\end{gathered}
$$ This gives: $$
\begin{aligned}
x_1 & =0\\
7 x^2+10 x^2-25&=0\\
a&=7 \\
b&=10 \\
c&=-25\\
x_{2,3} & =\frac{-10 \pm \sqrt{10^2-4(7)(-25)}}{2(7)} \\
& =\frac{-10 \pm \sqrt{800}}{14}\\
& =\frac{-5 \pm 10\sqrt 2}{7}.
\end{aligned}
$$ The solutions are: $$
\begin{aligned}
x_1&=0\\
x_2 & =\frac{-5 - 10\sqrt 2}{7} \\
& \approx -2.73459 \\
x_3 & =\frac{-5+ 10\sqrt 2}{7} \\
& \approx 1.30601.
\end{aligned}
$$ Define the following function and plot it. We see that the zeros are where they should be.
$$
f(x) =1.75 x^3+2.5 x^2-6.25 x.
$$
