6x/x+4=x-1

Solution for 6x/x+4=x-1 equation:

6x/x+4=x-1

We move all terms to the left:

6x/x+4-(x-1)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

6x/x-x+1+4=0

We multiply all the terms by the denominator


6x-x*x+1*x+4*x=0

We add all the numbers together, and all the variables

11x-x*x=0

Wy multiply elements

-1x^2+11x=0

a = -1; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-1)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-1}=\frac{-22}{-2}
=+11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-1}=\frac{0}{-2}
=0
$