x-7=-6+1/6x

Solution for x-7=-6+1/6x equation:

x-7=-6+1/6x

We move all terms to the left:

x-7-(-6+1/6x)=0


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(1/6x-6)-7=0

We get rid of parentheses

x-1/6x+6-7=0

We multiply all the terms by the denominator


x*6x+6*6x-7*6x-1=0

Wy multiply elements

6x^2+36x-42x-1=0

We add all the numbers together, and all the variables

6x^2-6x-1=0

a = 6; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·6·(-1)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{15}}{2*6}=\frac{6-2\sqrt{15}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{15}}{2*6}=\frac{6+2\sqrt{15}}{12}
$