Answer :
SOLUTION
Step1: Write out the equation
[tex]f(x)=-3x^2-4x+7[/tex]Apply quadratic formula method
Step2: write out the quadratic formula
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Step3: Identify the variable
from the function giving, compared with the general form of a quadratic equation
[tex]\begin{gathered} f(x)=ax^2+bx+c \\ \text{Then} \\ a=-3,b=-4,c=7 \end{gathered}[/tex]
Step4; Substitute the value of each variable into the formula
[tex]x=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(-3)(7)}}{2(-3)}[/tex]Step5: simplify the equation above
[tex]\begin{gathered} x=\frac{4\pm\sqrt[]{16+84}}{-6} \\ \\ x=\frac{4\pm\sqrt[]{10}}{-6} \\ \end{gathered}[/tex]Then, we have
[tex]\begin{gathered} x=\frac{4\pm10}{-6} \\ \\ x=\frac{4+10}{-6},\frac{4-10}{-6} \\ \\ x=\frac{14}{-6},\frac{-6}{-6} \end{gathered}[/tex]Therefore the value of x are
[tex]\begin{gathered} x=-\frac{7}{3},1 \\ \text{Then } \\ x=-\frac{7}{3},\text{ and 1} \end{gathered}[/tex]Therefore
Blank 1=-7/3
Blank 2=1