Question 969636
Put into general form, and either factor if possible, or use general solution for finding roots or quadratic expression.


{{{3x^2+9x-4<=0}}}


Try search for factorability:
(3x  2)(x  2)------2x and 3x------not useful.
(3x  1)(x   4)-------1x and 12x-----no useful.
(3x   4)(x   1 )-----4x and 3x------no use.
The quadratic expression is not factorable with simple integers.


Check discriminant:
{{{(9^2)-4*3*(-4)}}}
{{{81+16}}}
{{{97}}}


Roots are the critical values:
{{{(-9- sqrt(97))/6}}}   and   {{{(-9+ sqrt(97))/6}}}


You can check the three intervals of the x-axis to determine where is the solution.  Pick any single value in each of these intervals:
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{{{x<=(-9-sqrt(97))/6}}}
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{{{(-9-sqrt(97))/6<=x<=(-9+sqrt(97))/6}}}
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{{{(-9+sqrt(97))/6<=x}}}
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The exercise must be in the intermediate level because the quadratic part is not factorable and needs the general solution of finding roots for a quadratic expression for defining intervals.  No way trying to avoid starting with "{{{x^2}}}"  or what "<=" means.