In order to find the solution of this inequality, first let's find its roots:
[tex]\begin{gathered} 7x^2+35x=42 \\ 7x^2+35x-42=0 \\ x^2+5x-6=0 \\ a=1,b=5,c=-6 \\ \\ x_1=\frac{-b+\sqrt[]{b^2-4ac}}{2a}=\frac{-5+\sqrt[]{25-4\cdot1\cdot(-6)}}{2}=\frac{-5+\sqrt[]{49}}{2}=\frac{-5+7}{2}=1 \\ x_2=\frac{-b-\sqrt[]{b^2-4ac}}{2a}=\frac{-5-7}{2}=-6 \end{gathered}[/tex]
The roots are 1 and -6.
Since the concavity of this function is upwards (because a > 0), we have that the function is negative for value of x between the roots and positive for the other values (x < -6 or x > 1).
Since the inequality has the symbol "greater than or equal", we want the positive values, including zero, therefore the answer is x ≤ -6 or x ≥ 1 (option B).
