X+6+2=2/3x

Solution for X+6+2=2/3x equation:

X+6+2=2/3X

We move all terms to the left:

X+6+2-(2/3X)=0


Domain of the equation: 3X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(+2/3X)+6+2=0

We add all the numbers together, and all the variables

X-(+2/3X)+8=0

We get rid of parentheses

X-2/3X+8=0

We multiply all the terms by the denominator


X*3X+8*3X-2=0

Wy multiply elements

3X^2+24X-2=0

a = 3; b = 24; c = -2;
Δ = b2-4ac
Δ = 242-4·3·(-2)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-10\sqrt{6}}{2*3}=\frac{-24-10\sqrt{6}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+10\sqrt{6}}{2*3}=\frac{-24+10\sqrt{6}}{6}
$