Answer
$0.206, \ or, \ -2.404$
Work Step by Step
For the equation $23.8x^2 +52.3x-11.8= 0$, we use the quadratic formula as follows
$$
x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a},
\\
a=23.8, \quad b=52.3, \quad c=-11.8
.$$
That is, $$ x=\frac{-52.3\pm \sqrt{52.3^2-4(23.8)(-11.8)}}{2(23.8) }=0.206, \ or, \ -2.404
.$$
