Question

Solve the equation using any method you prefer. Give imaginary roots.
`3a^2+4=2a`

Answer 1

`3a^2+4=2a\\ 3a^2-2a+4=0\\ \Delta=(-2)^2-4\cdot3\cdot4=4-48=-44\\ √(\Delta)=√(-44)=2√(11)i\\ x_1=(-(-2)-2√(11)i)/(2\cdot3)=(2-2√(11)i)/(6)=(1-√(11)i)/(3)\\ x_2=(-(-2)+2√(11)i)/(2\cdot3)=(2+2√(11)i)/(6)=(1+√(11)i)/(3)\\`