SOLUTION:
We are to determine the equations that could be solved using quadratic formula;
[tex]\begin{gathered} (A)5x+4=3^{}x^4\text{ - 2} \\ 3^{}x^4\text{ - 5x - 2 -4 = 0} \\ 3^{}x^4\text{ - }5x\text{ - 6 = 0} \\ Since\text{ the highest power of x is 4, it can not be solved using quadratic method} \end{gathered}[/tex](B)
[tex]\begin{gathered} -x^2+4x+7=-x^2\text{ -9} \\ -x^2+x^2+4x+7\text{ + 9 = 0} \\ 4x\text{ + 16 = 0} \\ Since\text{ the highest power of x is 0, it can not be solved using quadratic method} \end{gathered}[/tex](C)
[tex]\begin{gathered} 9x+3x^2\text{ = 14 + x -1 = 0} \\ 3x^2\text{ + }9x\text{ - x -14 + 1 = 0} \\ 3x^2\text{ + 8x }-\text{ 13 = 0} \\ Since\text{ the highest power of x is 2, it can be solved using quadratic method.} \end{gathered}[/tex](d)
[tex]\begin{gathered} 2x^2+x^2\text{ +x = 30} \\ 3x^2\text{ + x = 30} \\ Since\text{ the highest power of x is 2, it can be solved using quadratic method} \end{gathered}[/tex]In conclusion, Options C and D can be solved using quadratic method.