Given the Quadratic Equation:
[tex]2x^2-9x+8=0[/tex]
You need to use the Quadratic Formula in order to solve it:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Notice that the equation is written in this form:
[tex]ax^2+bx+c=0[/tex]
Then, in this case:
[tex]\begin{gathered} a=2 \\ b=-9 \\ c=8 \end{gathered}[/tex]
Now you can substitute values into the formula and evaluate:
[tex]\begin{gathered} x=\frac{-(-9)\pm\sqrt{(-9)^2-4(2)(8)}}{(2)(2)} \\ \\ x=\frac{9\pm\sqrt{17}}{4} \end{gathered}[/tex]
Notice that you get two values:
[tex]x_1=\frac{9+\sqrt{17}}{4}[/tex][tex]x_2=\frac{9-\sqrt{17}}{4}[/tex]
Hence, the answer is:
[tex]x=\frac{9+\sqrt{17}}{4}\text{ or }x=\frac{9-\sqrt{17}}{4}[/tex]
