(240/x)-x=4

Solution for (240/x)-x=4 equation:

(240/x)-x=4

We move all terms to the left:

(240/x)-x-(4)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+240/x)-x-4=0

We add all the numbers together, and all the variables

-1x+(+240/x)-4=0

We get rid of parentheses

-1x+240/x-4=0

We multiply all the terms by the denominator


-1x*x-4*x+240=0

We add all the numbers together, and all the variables

-4x-1x*x+240=0

Wy multiply elements

-1x^2-4x+240=0

a = -1; b = -4; c = +240;
Δ = b2-4ac
Δ = -42-4·(-1)·240
Δ = 976
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:

$\sqrt{\Delta}=\sqrt{976}=\sqrt{16*61}=\sqrt{16}*\sqrt{61}=4\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{61}}{2*-1}=\frac{4-4\sqrt{61}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{61}}{2*-1}=\frac{4+4\sqrt{61}}{-2}
$