quadratic equation with absolute value

Lets say x is positive:

2x-3x+4=0

-1x+4=0.  I-4

-1x=-4

x=4

Now lets say x is negative:

(Im not sure about the answer)

First i try to isolate the absolute value x:

2x-3IxI+4=0.     I-2x

-3IxI+4=-2x.      I -4

-3IxI=-2x-4.       I/-3

IxI.  =. 2/3x. + 4/3x

So x = 2/3x+ 4/3x if x is positive, which gives u 4 if u plot it back into the equation or:

x=-(2/3x + 4/3x)

x= -2/3x -4/3x

if x is negativ.   

At this step im not really sure, so it can be false but if you plot this now back into the equation for IxI u get:

2x-3*(-2/3x - 4/3x)+4=0

Solve it and u get x=-0.5

So you got 2 answers of L{4, -0.5}

Both seem to work, but i guess theres a much easier way to get the result.

x^2 - 3|x| + 4 = 0

I don't  believe this has any "real" solutions......

See here :  https://www.desmos.com/calculator/pvwvwzobj7