#### Answer

The equation has two complex solutions.

#### Work Step by Step

$3x^{2}=4x-5$
Take all terms to the left side:
$3x^{2}-4x+5=0$
The discriminant is given by $b^{2}-4ac$. For this equation, $a=3$, $b=-4$ and $c=5$
Let the discriminant be $D$. Substitute the known values into the formula and evaluate:
$D=(-4)^{2}-4(3)(5)=16-60=-44$
Since the discriminant is equal to a negative number, the equation has two solutions and they are complex numbers.