#### Answer

The equation has two irrational solutions.

#### Work Step by Step

$4x^{2}=-6x+3$
Take all terms to the left side:
$4x^{2}+6x-3=0$
The discriminant is given by $b^{2}-4ac$. For this equation, $a=4$, $b=6$ and $c=-3$
Let the discriminant be $D$. Substitute the known values into the formula and evaluate:
$D=6^{2}-4(4)(-3)=36+48=84$
Since the discriminant is equal to a positive, non-perfect square number, the equation has two solutions and they are irrational numbers.