Step 1: Problem
[tex]\begin{gathered} -16x^2\text{ = 24x + 9} \\ 16x^2\text{ + 24x + 9 = 0} \end{gathered}[/tex]
Step 2: Concept
Apply the quadratic equation formula
[tex]x\text{ = }\frac{-b\text{ }\pm\text{ }\sqrt[]{b^2\text{ - 4ac}}}{2a}[/tex]
Step 3: Method
a = 16
b = 24
c = 9
[tex]\begin{gathered} x\text{ = }\frac{-\text{ 24 }\pm\text{ }\sqrt[]{24^2\text{ - 4 }\times\text{ 16 }\times\text{ 9}}}{2\text{ }\times\text{ 16}} \\ x\text{ = }\frac{-\text{ 24 }\pm\text{ }\sqrt[]{576\text{ - 576}}}{32} \\ x\text{ = }\frac{\text{ - 24 }\pm\text{ }\sqrt[]{0}}{32} \\ x\text{ = }\frac{-\text{ 24 }\pm\text{ 0}}{32} \\ x\text{ = }\frac{-\text{ 24 + 0}}{32}\text{ or }\frac{-24\text{ - 0}}{32} \\ x\text{ = }\frac{-24}{32}\text{ or }\frac{-\text{ 24}}{32} \\ x\text{ = }\frac{-3}{4}\text{ twice} \end{gathered}[/tex]
