60/x-4=x

Solution for 60/x-4=x equation:

60/x-4=x

We move all terms to the left:

60/x-4-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1x+60/x-4=0

We multiply all the terms by the denominator


-1x*x-4*x+60=0

We add all the numbers together, and all the variables

-4x-1x*x+60=0

Wy multiply elements

-1x^2-4x+60=0

a = -1; b = -4; c = +60;
Δ = b2-4ac
Δ = -42-4·(-1)·60
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{-(-4)-16}{2*-1}=\frac{-12}{-2}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+16}{2*-1}=\frac{20}{-2}
=-10
$