Answer
No real number solutions.
Work Step by Step
Step 1: Comparing $3x^{2}-2x+5=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we find:
$a=3$, $b=-2$ and $c=5$
Step 2: The quadratic formula is:
$x=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$
Step 3: Substituting the values of a, b and c in the formula:
$x=\frac{-(-2) \pm \sqrt {(-2)^{2}-4(3)(5)}}{2(3)}$
Step 4: $x=\frac{2 \pm \sqrt {4-60}}{6}$
Step 5: $x=\frac{2 \pm \sqrt {-56}}{6}$
The square root of -56 is not a real number, so there are no real number solutions.
