2/x-2=18x+6

Solution for 2/x-2=18x+6 equation:

2/x-2=18x+6

We move all terms to the left:

2/x-2-(18x+6)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

2/x-18x-6-2=0

We multiply all the terms by the denominator


-18x*x-6*x-2*x+2=0

We add all the numbers together, and all the variables

-8x-18x*x+2=0

Wy multiply elements

-18x^2-8x+2=0

a = -18; b = -8; c = +2;
Δ = b2-4ac
Δ = -82-4·(-18)·2
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{13}}{2*-18}=\frac{8-4\sqrt{13}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{13}}{2*-18}=\frac{8+4\sqrt{13}}{-36}
$