Answer:
[tex]x=0.75 \pm 2.47067i[/tex]
Step-by-step explanation:
Quadratic Formula: [tex]x=\frac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]
√-1 is imaginary number i
Step 1: Define
y = -3x² + 4.5x - 20
a = -3
b = 4.5
c = -20
Step 2: Substitute and Evaluate
[tex]x=\frac{-4.5 \pm \sqrt{4.5^2-4(-3)(-20)} }{2(-3)}[/tex]
[tex]x=\frac{-4.5 \pm \sqrt{20.25-240} }{-6}[/tex]
[tex]x=\frac{-4.5 \pm \sqrt{-219.75} }{-6}[/tex]
[tex]x=\frac{-4.5 \pm \sqrt{219.75}(\sqrt{-1} ) }{-6}[/tex]
[tex]x=\frac{-4.5 \pm i\sqrt{219.75} }{-6}[/tex]
[tex]x=\frac{4.5 \pm i14.824 }{6}[/tex]
[tex]x=0.75 \pm 2.47067i[/tex]
