Answer
Solution set: $\displaystyle \{-1, \frac{3}{2}\}$
Work Step by Step
Quadratic formula, a=$2$, b=$-1$, c=$-3$
$x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
Checking $\Delta=b^{2}-4ac=1-4(2)(-3)=1+24=25$
$\Delta$ is positive, so there will be 2 real solutions.
$x=\displaystyle \frac{-(-1)\pm\sqrt{25}}{2(2)}=\frac{1\pm 5}{4}$
$x=\displaystyle \frac{1-5}{4}=\frac{-4}{4}=-1$
or
$x=\displaystyle \frac{1+5}{4}=\frac{6}{4}=\frac{3}{2}$
Solution set: $\displaystyle \{-1, \frac{3}{2}\}$
