Question 344800
Hi, 
re: Your question
 so I still don't understand how online calculators are getting x= 0.83333 +- 0.79930i. Where does the .83333 come from? "I understand that root(-23) = .79930i, but cannot figure out .83333"
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online calculators are following thru with the division by the 6 in the denominator
 -(-5)/2*3  or 5/6 is .83333 
sqrt(-)23*i /2*3 = +-4.79583*i /6 = +-.79930i
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Hi, it does end up with a square root of a negative number(-23):  See below:
That means there are no solutions among real numbers.

{{{3x^2-5x+4}}}
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Using Quadratic Formaula to solve:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
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*[invoke quadratic "x", 3, -5, 4]