x-2/3x+4=2

Solution for x-2/3x+4=2 equation:

x-2/3x+4=2

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x-2/3x+2=0

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2+6x-2=0

a = 3; b = 6; c = -2;
Δ = b2-4ac
Δ = 62-4·3·(-2)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{15}}{2*3}=\frac{-6-2\sqrt{15}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{15}}{2*3}=\frac{-6+2\sqrt{15}}{6}
$