how do i find x?

So I do not know about you but I hate fractions so you can get rid of the fraction -4/3 and 4/9 have a commen denomeator of 9 so if you multiply the equation by 9 or in other words 9(-4/3 x+4/9=-x^2) Then you have 12x+4=-9x^2. This is a quadratic so you need to set 1 side to 0. This can be done by adding 9x^2 to both sides. Then you have 9x^2-12x+4=-9x^2+9x^2. Then we have 9x^2-12x+4=0. I learned this cool way to factor a quadratic ax^2+bx+c=0. You ask yourself what factors of ac add up to give you b. In this case ac=9(4)=36=-6(-6) and -6-6=-12

Then 9x^2-12x+4=0 becomes

9x^2-6x-6x+4=0 and ask what do the 1st and 2nd have in commen well they have a 3x and ask what do the 3rd and 4th have in commen well they have a -2 then it becomes

3x(3x-2)-2(3x-2)=0 Then

(3x-2)(3x-2)=0 Then

(3x-2)^2=0 Then

3x-2=0 Then

3x=2 Then

x=2/3