Answer:
[tex]x=\dfrac{7\pm\sqrt{17}}{4}[/tex]
Step-by-step explanation:
First of all, write the equation in standard form. Then identify a, b, c and fill in the values in the formula.
[tex]4x^2-9x=2x^2-2x-4\\\\4x^2 -9x -(2x^2-2x-4) = 0\quad\text{subtract right side}\\\\4x^2-9x-2x^2+2x+4=0\quad\text{eliminate parentheses}\\\\2x^2 -7x+4=0\quad\text{collect terms; a=2, b=-7, c=4}\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\quad\text{quadratic formula}\\\\x=\dfrac{-(-7)\pm\sqrt{(-7)^2-4(2)(4)}}{2(2)}\quad\text{fill in a, b, c}\\\\\boxed{x=\dfrac{7\pm\sqrt{17}}{4}}\quad\text{simplify}[/tex]
