Question 182677
{{{12x^2-10x-42=0}}}
1. Quadratic formula,
 {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (-(-10) +- sqrt( (-10)^2-4*12*(-42) ))/(2*12) }}}
{{{x = (10 +- sqrt(100+2016 ))/(24) }}}
{{{x = (10 +- sqrt(2116 ))/(24) }}}
{{{x = (10 +- 46)/(24) }}}

{{{x[1] = (10 + 46)/(24) }}}
{{{x[1] = (56)/(24) }}}
{{{highlight(x[1] = 7/3) }}}
{{{x[2] = (10 - 46)/(24) }}}
{{{x[2] = (-36)/(24) }}}
{{{highlight(x[2]=-(3/2))}}}
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2. Factor the equation,
{{{12x^2-10x-42=0}}}
{{{(4x+6)(3x-7)=0}}}
First solution:
{{{4x+6=0}}}
{{{4x=-6}}}
{{{x=-(6/4)=-(3/2)}}}
Second solution:
{{{3x-7=0}}}
{{{3x=7}}}
{{{x=7/3}}}
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3. Graph and make reasonable guesses. 
{{{ graph( 300, 300, -2, 4, -2, 2, 12x^2-10x-42) }}}
Iterate until you find the answer. 
Although it's easy for this equation, it may not be the best method for every equation.