(540/x)-2x=6

Solution for (540/x)-2x=6 equation:

(540/x)-2x=6

We move all terms to the left:

(540/x)-2x-(6)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+540/x)-2x-6=0

We add all the numbers together, and all the variables

-2x+(+540/x)-6=0

We get rid of parentheses

-2x+540/x-6=0

We multiply all the terms by the denominator


-2x*x-6*x+540=0

We add all the numbers together, and all the variables

-6x-2x*x+540=0

Wy multiply elements

-2x^2-6x+540=0

a = -2; b = -6; c = +540;
Δ = b2-4ac
Δ = -62-4·(-2)·540
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-66}{2*-2}=\frac{-60}{-4}
=+15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+66}{2*-2}=\frac{72}{-4}
=-18
$