X+6/3x=13/3x

Solution for X+6/3x=13/3x equation:

X+6/3X=13/3X

We move all terms to the left:

X+6/3X-(13/3X)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R



Domain of the equation: 3X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X+6/3X-(+13/3X)=0

We get rid of parentheses

X+6/3X-13/3X=0

We multiply all the terms by the denominator


X*3X+6-13=0

We add all the numbers together, and all the variables

X*3X-7=0

Wy multiply elements

3X^2-7=0

a = 3; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·3·(-7)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{21}}{2*3}=\frac{0-2\sqrt{21}}{6}
=-\frac{2\sqrt{21}}{6}
=-\frac{\sqrt{21}}{3}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{21}}{2*3}=\frac{0+2\sqrt{21}}{6}
=\frac{2\sqrt{21}}{6}
=\frac{\sqrt{21}}{3}
$