Answer
$2$ real irrational distinct solutions
Work Step by Step
Bring the equation to the standard form by moving all terms on one side:
$$\begin{align*}
2x^2+4x-3&=0.
\end{align*}$$
To determine the number and the type of the solutions for the equation $ax^2+bx+c=0$, we have to calculate the discriminant $\Delta=b^2-4ac$ and compare it to zero.
Identify $a$, $b$, $c$:
$$\begin{align*}
a&=2\\
b&=4\\
c&=-3.
\end{align*}$$
Calculate the discriminant:
$$\begin{align*}
\Delta=4^2-4(2)(-3)=40.
\end{align*}$$
Because $\Delta>0$, the equation has $2$ real distinct solutions.
Because $\Delta$ is not a perfect square, the solutions are irrational.
So the equation has $2$ real irrational distinct solutions.