The roots of the quadratic equation \(10x^2 - 13x - 3 = 0\) can be found using the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a = 10\), \(b = -13\), and \(c = -3\).

Substituting these values into the formula gives:

\(x = \frac{-(-13) \pm \sqrt{(-13)^2 - 4*10*(-3)}}{2*10}\)

Solving this gives:

\(x = \frac{13 \pm \sqrt{169 + 120}}{20} = \frac{13 \pm \sqrt{289}}{20} = \frac{13 \pm 17}{20}\)

So, the roots of the equation are:

\(x = \frac{30}{20} = \frac{3}{2}\) and \(x = \frac{-4}{20} = -\frac{1}{5}\)