Answer
$4.22, \ or, \ -1.72
.$
Work Step by Step
For the equation $4x^2 -10x-29 = 0$, we use the quadratic formula as follows
$$
x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a},
\\
a=4, \quad b=-10, \quad c=-29
.$$
That is, $$ x=\frac{10 \pm \sqrt{100+4(4)(29)}}{8 }=4.22, \ or, \ -1.72
.$$
