x+8-2/3x=-2

Solution for x+8-2/3x=-2 equation:

x+8-2/3x=-2

We move all terms to the left:

x+8-2/3x-(-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+10=0

We multiply all the terms by the denominator


x*3x+10*3x-2=0

Wy multiply elements

3x^2+30x-2=0

a = 3; b = 30; c = -2;
Δ = b2-4ac
Δ = 302-4·3·(-2)
Δ = 924
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:

$\sqrt{\Delta}=\sqrt{924}=\sqrt{4*231}=\sqrt{4}*\sqrt{231}=2\sqrt{231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{231}}{2*3}=\frac{-30-2\sqrt{231}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{231}}{2*3}=\frac{-30+2\sqrt{231}}{6}
$