(2x/1x)-x=18

Solution for (2x/1x)-x=18 equation:

(2x/1x)-x=18

We move all terms to the left:

(2x/1x)-x-(18)=0


Domain of the equation: 1x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+2x/1x)-x-18=0

We add all the numbers together, and all the variables

-1x+(+2x/1x)-18=0

We get rid of parentheses

-1x+2x/1x-18=0

We multiply all the terms by the denominator


-1x*1x+2x-18*1x=0

We add all the numbers together, and all the variables

2x-1x*1x-18*1x=0

Wy multiply elements

-1x^2+2x-18x=0

We add all the numbers together, and all the variables

-1x^2-16x=0

a = -1; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-1)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-1}=\frac{32}{-2}
=-16
$