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To solve the equation \(1.7x^2 - 1.2x - 2.1 = 0\), we can use the quadratic formula. The quadratic formula states that for an equation of the form \(ax^2 + bx + c = 0\), the solutions for \(x\) are given by:

\[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]

In this case, \(a = 1.7\), \(b = -1.2\), and \(c = -2.1\). Substituting these values into the quadratic formula, we have:

\[x = \frac{-(-1.2) \pm \sqrt{(-1.2)^2 - 4(1.7)(-2.1)}}{2(1.7)}\]

Simplifying inside the square root:

\[x = \frac{1.2 \pm \sqrt{1.44 + 14.28}}{3.4}\]

\[x = \frac{1.2 \pm \sqrt{15.72}}{3.4}\]

\[x = \frac{1.2 \pm 3.96}{3.4}\]

Now we have two possible solutions:

\[x_1 = \frac{1.2 + 3.96}{3.4} \approx 1.41\]

\[x_2 = \frac{1.2 - 3.96}{3.4} \approx -0.71\]

Therefore, the solutions to the equation \(1.7x^2 - 1.2x - 2.1 = 0\) are approximately \(x = 1.41\) and \(x = -0.71\).