Answer:
Nico is incorrect because he added 3x instead of subtracting 3x from both sides.
[tex]x=-\frac{1+i\sqrt{23} }{2} , -\frac{1-i\sqrt{23} }{2}[/tex]
Step-by-step explanation:
Ok, so first we need to get the equation set to 0 so we have a quadratic equation.
[tex]4x+6=3x-x^{2} \\x^{2} +4x+6=3x\\x^{2}+x+6=0\\[/tex]
Here you would begin to factor but this is not possible with this equation. There is not a solution set that would be a product of 6 and a sum of 1. So you have to use the quadratic formula.
[tex]\frac{-b\pm \sqrt{b^{2}-4ac } }{2a}[/tex]
So if we look at our quadratic,
[tex](1)x^{2}+(1)x+6=0\\[/tex]
[tex]ax^{2} +bx+c=0[/tex]
we know,
[tex]a=1\\b=1\\c=6[/tex]
Now it's time to plug and play.
[tex]\frac{-(1)\pm \sqrt{(1)^{2}-4(1)(6) } }{2(1)}\\\frac{-1\pm \sqrt{1-24 } }{2}\\\frac{-1\pm \sqrt{-23 } }{2}[/tex]
Ok, so it is impossible to have a negative root which means we have a complex number or imaginary number. We use [tex]i[/tex] to represent these imaginary numbers. We can't simplify the root anymore.
[tex]\frac{-1\pm i\sqrt{23 } }{2}[/tex]
