Question 150123
Yes, there are a lot of steps. 
You started out with a mistake in the denominator, 19 instead of 3.
{{{x=(-19+-sqrt((-19)^2-4*3*(-14)))/(2*highlight(3))}}}
and made a minor mistake along the way. 
{{{x=(highlight(-19)+-sqrt(361+168))/6}}} 
You lost the negative sign in front of 19.
{{{x=(-19+-sqrt(529))/6}}}
{{{x=(-19 +- 23)/6}}}
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First solution
{{{x=(-19+23)/6}}}
{{{x=4/6}}}
{{{x=2/3}}} Answer in lowest terms
Second solution
{{{x=(-19-23)/6}}}
{{{x=-42/6}}}
{{{x=-7}}} Answer in lowest terms
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I'm not sure about x=6/2=-4??
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Remember you can always check your answer by plugging it back into the equation.
{{{3x^2+19x-14=0}}}
{{{3(-7)^2+19(-7)-14=0}}}
{{{147-133-14=0}}}
{{{0=0}}}
Good answer.