Answer:
Solving the equation [tex]3r^2-2r=-9[/tex] using quadratic formula we get: [tex]\mathbf{ r=\frac{1+\sqrt{26}\:i}{3}\:or\: r=\frac{1-\sqrt{26}\:i}{3}}[/tex]
Step-by-step explanation:
We need to solve the equation [tex]3r^2-2r=-9[/tex] using quadratic formula.
The quadratic formula is: [tex]r=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
For the given equation: [tex]3r^2-2r=-9[/tex]
We can write it as: [tex]3r^2-2r+9=0[/tex]
We have a = 3, b= -2 and c=9
Putting values in quadratic formula and finding value of r
[tex]r=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\r=\frac{-(-2)\pm\sqrt{(-2)^2-4(3)(9)}}{2(3)}\\r=\frac{2\pm\sqrt{4-108}}{6}\\r=\frac{2\pm\sqrt{-104}}{6}\\We\:know\:that: \sqrt{-1}=i\\ r=\frac{2\pm\sqrt{26} \:i}{6}\\ r=\frac{2+2\sqrt{26}\:i}{6}\:or\: r=\frac{2-2\sqrt{26}\:i}{6}\\ r=\frac{2(1+\sqrt{26}\:i)}{6}\:or\: r=\frac{2(1-\sqrt{26}\:i)}{6}\\ r=\frac{1+\sqrt{26}\:i}{3}\:or\: r=\frac{1-\sqrt{26}\:i}{3}[/tex]
So, solving the equation [tex]3r^2-2r=-9[/tex] using quadratic formula we get: [tex]\mathbf{ r=\frac{1+\sqrt{26}\:i}{3}\:or\: r=\frac{1-\sqrt{26}\:i}{3}}[/tex]
