-1/3x+21=-x+7

Solution for -1/3x+21=-x+7 equation:

-1/3x+21=-x+7

We move all terms to the left:

-1/3x+21-(-x+7)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-1/3x-(-1x+7)+21=0

We get rid of parentheses

-1/3x+1x-7+21=0

We multiply all the terms by the denominator


1x*3x-7*3x+21*3x-1=0

Wy multiply elements

3x^2-21x+63x-1=0

We add all the numbers together, and all the variables

3x^2+42x-1=0

a = 3; b = 42; c = -1;
Δ = b2-4ac
Δ = 422-4·3·(-1)
Δ = 1776
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:

$\sqrt{\Delta}=\sqrt{1776}=\sqrt{16*111}=\sqrt{16}*\sqrt{111}=4\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-4\sqrt{111}}{2*3}=\frac{-42-4\sqrt{111}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+4\sqrt{111}}{2*3}=\frac{-42+4\sqrt{111}}{6}
$