Given:
[tex]6x^2\text{ - 14x - 9 = 0}[/tex]
The quadratic formula is defined as:
[tex]x\text{ = }\frac{-b\text{ }\pm\sqrt[]{b^2-4ac}}{2a}[/tex]
given that the general form of a quadratic equation is:
[tex]ax^2\text{ + bx + c = 0}[/tex]
Hence:
a = 6, b = -14, c = -9
Substituting into the formula:
[tex]x\text{ = }\frac{-(-14)\text{ }\pm\sqrt[]{(-14)^2\text{ -4(6)(-9)}}}{2\times6}[/tex]
Simplifying we have:
[tex]\begin{gathered} x\text{ = }\frac{14\text{ }\pm\text{ }\sqrt[]{412}}{12} \\ =\text{ }\frac{14\text{ }\pm\text{ }\sqrt[]{412}}{12} \\ =\text{ }\frac{14\text{ }\pm\text{ 2}\sqrt[]{103}}{12} \\ =\text{ }\frac{7\text{ }\pm\sqrt[]{103}}{6} \end{gathered}[/tex]
Answer:
[tex]x\text{ = }\frac{7\text{ + }\sqrt[]{103}}{6}\text{ or }\frac{7\text{ - }\sqrt[]{103}}{6}[/tex]
