Answer
$\left\{-\dfrac{3}{2},-1\right\}$
Work Step by Step
The equation is in standard form $ax^2+bx+c=0$.
We have $a=2,b=5$ and $c=3$.
The discriminant is
$=b^2-4ac$
$=(5)^2-4(2)(3)$
$=25-24$
$=1$
Since $1>0$. There are two real solutions.
The quadratic formula is
$x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$
Substitute the values of $a, b, c,$ and the discriminant into the quadratic formula to obtain:
$x=\dfrac{-(5)\pm \sqrt{(1)}}{2(2)}$
Simplify.
$x=\dfrac{-5\pm 1}{4}$
Split the expression to obtain:
$x=\dfrac{-5- 1}{4}\quad $ or $\quad x=\dfrac{-5+1}{4}$
$x=\dfrac{-6}{4}\quad $ or $\quad x=\dfrac{-4}{4}$
$x=-\dfrac{3}{2}\quad $ or $\quad x=-1$
The solution set is $\left\{-\dfrac{3}{2},-1\right\}$.
