108/x=x-3

Solution for 108/x=x-3 equation:

108/x=x-3

We move all terms to the left:

108/x-(x-3)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

108/x-x+3=0

We multiply all the terms by the denominator


-x*x+3*x+108=0

We add all the numbers together, and all the variables

3x-x*x+108=0

Wy multiply elements

-1x^2+3x+108=0

a = -1; b = 3; c = +108;
Δ = b2-4ac
Δ = 32-4·(-1)·108
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-21}{2*-1}=\frac{-24}{-2}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+21}{2*-1}=\frac{18}{-2}
=-9
$