Solve by using factoring or quadratic equation?

Question

hi, i seem to not get this problem.


The problem:
x^2/2 + 1= 2x/3

I got this:

using standard form multiply by 6,

3x^2 - 4x +6=0 then quadratic formula

I get 4/6+- Squr-root 16-4(3)(6)/6, over 6..


real answer is 2+- i squr-root 14/3

thanks

i don't understand how to get the "2" in the last step?

4+- 2 sqrt-14/3

SOLVED, thanks nayanmange

Answer 1

[4 +- sqrt 16 - (4)(3)(6)] / 6
[4 +- sqrt 56 ] / 6
[4 +- 2 sqrt 14*(-1) ] / 6

Now, square root of -1 is defined as iota ( i )

[4 +- 2i sqrt 14] / 6
= [2 +- i sqrt 14] / 3

Answer 2

3x² - 4x + 6 = 0
x = [ 4 ± √(16 - 72)] / 6
x = [ 4 ± √ (- 56)] / 6
x = [ 4 ± √ (4 x - 14)] / 6
x = [ 4 ± 2√ ( - 14) ] / 6
x = [ 2 ± √ ( - 14) ] / 3
x = [ 2 ± √ (14 i ²) ] / 3-------(where i² = -1)
x = [ 2 ± i √ 14 ] / 3