Question 134150
{{{12x^3 - 77x^2 + 91x - 30 = 0}}} 
Substitute {{{(2/3)*x^2 for x^3}}}
Substitute {{{(2/3)*x for x^2}}}
Substitute {{{2/3 for x}}}
{{{12x^2*(2/3) - 77x*(2/3) + 91*(2/3) - 30 = 0}}}
Multiply both sides by {{{3/2}}}
{{{12x^2 - 77x + 91 - 45 = 0}}}
{{{12x^2 - 77x + 46 = 0}}}
Use quadratiic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (-(-77) +- sqrt( (-77)^2-4*12*46 ))/(2*12) }}}
{{{x = (77 +- sqrt(3721))/24 }}}
{{{x = (77 +- 61) / 24}}}
{{{x = 19/12}}}
{{{x = 2/3}}}
The roots are {{{x = 19/12}}}, {{{x = 2/3}}}, {{{x = 2/3}}}
{{{x = 2/3}}} is a double root.