Answer
$$ \frac{3}{2}, \ or, \ -4
.$$
Work Step by Step
For the equation $2x^2 +5x -12= 0$, we use the quadratic formula as follows
$$
x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a},
\\
a=2, \quad b=5, \quad c=-12
.$$
That is, $$ x=\frac{-5 \pm \sqrt{25+96}}{4 }=\frac{-5 \pm11}{4 }= \frac{3}{2}, \ or, \ -4
.$$
Check the result:
$$
2(4^2)-20-12=12-12=0, \quad
2((3/2)^2)+5(3/2)-12=12-12=0.
$$
