X-3=1/3x+13

Solution for X-3=1/3x+13 equation:

X-3=1/3X+13

We move all terms to the left:

X-3-(1/3X+13)=0


Domain of the equation: 3X+13)!=0

X∈R


We get rid of parentheses

X-1/3X-13-3=0

We multiply all the terms by the denominator


X*3X-13*3X-3*3X-1=0

Wy multiply elements

3X^2-39X-9X-1=0

We add all the numbers together, and all the variables

3X^2-48X-1=0

a = 3; b = -48; c = -1;
Δ = b2-4ac
Δ = -482-4·3·(-1)
Δ = 2316
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:

$\sqrt{\Delta}=\sqrt{2316}=\sqrt{4*579}=\sqrt{4}*\sqrt{579}=2\sqrt{579}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{579}}{2*3}=\frac{48-2\sqrt{579}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{579}}{2*3}=\frac{48+2\sqrt{579}}{6}
$