x+3=7-(1/3x)

Solution for x+3=7-(1/3x) equation:

x+3=7-(1/3x)

We move all terms to the left:

x+3-(7-(1/3x))=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-(7-(+1/3x))+3=0

We multiply all the terms by the denominator


x*3x))-(7-(+3*3x))+1=0

Wy multiply elements

3x^2+9x=0

a = 3; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·3·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*3}=\frac{-18}{6}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*3}=\frac{0}{6}
=0
$