-8+(4x/x+1)=-6x

Solution for -8+(4x/x+1)=-6x equation:

-8+(4x/x+1)=-6x

We move all terms to the left:

-8+(4x/x+1)-(-6x)=0


Domain of the equation: x+1)!=0

x∈R


We get rid of parentheses

4x/x+6x+1-8=0

We multiply all the terms by the denominator


4x+6x*x+1*x-8*x=0

We add all the numbers together, and all the variables

-3x+6x*x=0

Wy multiply elements

6x^2-3x=0

a = 6; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·6·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*6}=\frac{6}{12}
=1/2
$