The Solution:
Given:
[tex]4m^2-7m+2=5[/tex]
We are required to use the Quadratic Formula to solve the equation above.
[tex]\begin{gathered} 4m^2-7m+2-5=0 \\ 4m^2-7m-3=0 \end{gathered}[/tex]
The Quadratic Formula is:
[tex]m=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
In this case:
[tex]\begin{gathered} a=4 \\ b=-7 \\ c=-3 \end{gathered}[/tex]
Substitute:
[tex]m=\frac{-(-7)\pm\sqrt{(-7)^2-4(4)(-3)}}{2(4)}[/tex][tex]m=\frac{7\pm\sqrt{49+48}}{8}=\frac{7\pm\sqrt{97}}{8}[/tex]
Therefore, the correct answer is [option A]
