/x-6=7x+1

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

/x-6=7x+1

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We get rid of parentheses

/x-7x-1-6=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-7x-7x*x=0

Wy multiply elements

-7x^2-7x=0

a = -7; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-7)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-7}=\frac{0}{-14}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-7}=\frac{14}{-14}
=-1
$