Answer
$\color{blue}{\bf{76\text{; two distinct irrational solutions}}}$
Work Step by Step
Add $3$ to both sides to obtain:
$$-6x^2+2x+3=0$$
This this equation has $a=-6$, $b=2$, and $x=3$.
RECALL:
(1) The discriminant is equal to $b^2-4ac$.
(2) A quadratic equation has the following types of solutions based on the value of the discriminant:
(a) when $b^2-4ac$ is a $\bf{\text{positive perfect square}}$, the equation has $\bf{\text{two distinct rational solutions}}$;
(b) when $b^2-4ac$ is a $\bf{\text{positive but not a perfect square}}$, the equation has $\bf{\text{two distinct irrational solutions}}$;
(c) when $b^2-4ac$ is $\bf{0}$, the equation has $\bf{\text{one rational solution (a double solution)}}$;
(d) when $b^2-4ac$ is $\bf{\text{negative}}$, the equation has $\bf{\text{two distinct non-real complex solutions}}$;
The discriminant of the equation above is:
$$b^2-4ac$$ $$2^2 - 4(-6)(3)$$ $$4+72=\color{blue}{\bf{76}}$$
The discriminant is $\bf{\text{positive but not a perfect square}}$.
Thus, the given equation has $\color{blue}{\bf{\text{two distinct irrational solutions.}}}$
