6/x-8=2x+6

Solution for 6/x-8=2x+6 equation:

6/x-8=2x+6

We move all terms to the left:

6/x-8-(2x+6)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

6/x-2x-6-8=0

We multiply all the terms by the denominator


-2x*x-6*x-8*x+6=0

We add all the numbers together, and all the variables

-14x-2x*x+6=0

Wy multiply elements

-2x^2-14x+6=0

a = -2; b = -14; c = +6;
Δ = b2-4ac
Δ = -142-4·(-2)·6
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{61}}{2*-2}=\frac{14-2\sqrt{61}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{61}}{2*-2}=\frac{14+2\sqrt{61}}{-4}
$