x+5=1/3x+5

Solution for x+5=1/3x+5 equation:

x+5=1/3x+5

We move all terms to the left:

x+5-(1/3x+5)=0


Domain of the equation: 3x+5)!=0

x∈R


We get rid of parentheses

x-1/3x-5+5=0

We multiply all the terms by the denominator


x*3x-5*3x+5*3x-1=0

Wy multiply elements

3x^2-15x+15x-1=0

We add all the numbers together, and all the variables

3x^2-1=0

a = 3; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·3·(-1)
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{3}}{2*3}=\frac{0-2\sqrt{3}}{6}
=-\frac{2\sqrt{3}}{6}
=-\frac{\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{3}}{2*3}=\frac{0+2\sqrt{3}}{6}
=\frac{2\sqrt{3}}{6}
=\frac{\sqrt{3}}{3}
$