Answer:
[tex]x\in[-2.84,1.17][/tex]
Step-by-step explanation:
The first, we will write our inequality in another form:
[tex]3x^2-4\leq 6-5x[/tex]
[tex]3x^2-4-6+5x\leq 0[/tex]
[tex]3x^2+5x-10\leq 0[/tex]
We want to know when is it equal to 0.
First we solve the equation [tex]3x^2+5x-10=0[/tex]:
[tex]x_{1,2}=\frac{-5+-\sqrt{25+120}}{6}[/tex]
[tex]x_{1,2}=\frac{-5+-12.04}{6}[/tex]
[tex]x_1=1.17[/tex]
[tex]x_2=-2.84[/tex]
So we want to know when [tex]3x^2+5x-10\leq 0[/tex] is true. We know, when a>0 function is negative when x is between two zeros. In our example a=3>0. Then we have:
It is true if [tex]x\in[-2.84,1.17][/tex]
