x-23=1/3x-7

Solution for x-23=1/3x-7 equation:

x-23=1/3x-7

We move all terms to the left:

x-23-(1/3x-7)=0


Domain of the equation: 3x-7)!=0

x∈R


We get rid of parentheses

x-1/3x+7-23=0

We multiply all the terms by the denominator


x*3x+7*3x-23*3x-1=0

Wy multiply elements

3x^2+21x-69x-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}
$