Question

how do you solve 2/3 x squared + x= 4 + 2/3

Answer 1

This?
\[\frac{2}{3}x^{2}+x= 4+\frac{2}{3}\]

Answer 2

yeah that

Answer 3

When you have a polynomial like this, you want to get everything on one side so it equals 0:\[\frac{2}{3}x^{2} + x = \frac{14}{3}\]\[\frac{2}{3}x^{2} + \frac{3}{3}x - \frac{14}{3} = 0\]
Then to make it easier, you can divide the whole thing by 3:\[2x^{2} + 3x -14 = 0\]
Then you can factor it:\[(2x+7)(x-2)=0\]
And now it can be solved, because for this to be zero, at least one of the parentheses needs to equal 0. So solve the first parentheses:
\[(2x+7) = 0\]\[2x = -7\]\[x = -\frac{7}{2}\]
Then the 2nd:\[(x-2) = 0\]\[x=2\]
So you have 2 values that would work for x: -7/2 and 2