The quadratic formula is:
[tex]\begin{gathered} \frac{\text{ -}b\pm\sqrt[2]{b^2\text{ -4ac}}}{2a} \\ The\text{ }equation\text{ }is: \\ 2x^2+3x\text{ -}5=4 \\ 2x^2+3x\text{ -}5\text{ -4=0} \end{gathered}[/tex]We need to equal to zero before using the formula.
Noah's mistake was that he stated c=-5 when c= -9
[tex]\begin{gathered} \frac{\text{ -}b\pm\sqrt{b^2\text{ -4ac}}}{2a} \\ =\frac{-3\pm\sqrt{(\text{ -3\rparen}^2\text{ -4\lparen2\rparen\lparen-9\rparen}}}{2(2)} \\ =\frac{-3\pm\sqrt{9\text{ +72}}}{4} \\ =\frac{-3\pm\sqrt{81}}{4} \\ =\frac{-3\pm9}{4} \\ \\ x1=\frac{-3+9}{4} \\ =\frac{6}{4}=\frac{3}{2}=1.5 \\ \\ x2=\frac{-3-9}{4} \\ =\frac{-12}{4} \\ =\text{ -3} \end{gathered}[/tex]x = 1.5 or x = -3
