x^2+2x/3=2

Solution for x^2+2x/3=2 equation:

x^2+2x/3=2

We move all terms to the left:

x^2+2x/3-(2)=0

We multiply all the terms by the denominator


x^2*3+2x-2*3=0

We add all the numbers together, and all the variables

x^2*3+2x-6=0

Wy multiply elements

3x^2+2x-6=0

a = 3; b = 2; c = -6;
Δ = b2-4ac
Δ = 22-4·3·(-6)
Δ = 76
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{19}}{2*3}=\frac{-2-2\sqrt{19}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{19}}{2*3}=\frac{-2+2\sqrt{19}}{6}
$