-1/3x-7=x+5

Solution for -1/3x-7=x+5 equation:

-1/3x-7=x+5

We move all terms to the left:

-1/3x-7-(x+5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

-1/3x-x-5-7=0

We multiply all the terms by the denominator


-x*3x-5*3x-7*3x-1=0

Wy multiply elements

-3x^2-15x-21x-1=0

We add all the numbers together, and all the variables

-3x^2-36x-1=0

a = -3; b = -36; c = -1;
Δ = b2-4ac
Δ = -362-4·(-3)·(-1)
Δ = 1284
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:

$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{321}}{2*-3}=\frac{36-2\sqrt{321}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{321}}{2*-3}=\frac{36+2\sqrt{321}}{-6}
$