180/x-3=x

Solution for 180/x-3=x equation:

180/x-3=x

We move all terms to the left:

180/x-3-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1x+180/x-3=0

We multiply all the terms by the denominator


-1x*x-3*x+180=0

We add all the numbers together, and all the variables

-3x-1x*x+180=0

Wy multiply elements

-1x^2-3x+180=0

a = -1; b = -3; c = +180;
Δ = b2-4ac
Δ = -32-4·(-1)·180
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-27}{2*-1}=\frac{-24}{-2}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+27}{2*-1}=\frac{30}{-2}
=-15
$