2x-12=144/x

Solution for 2x-12=144/x equation:

2x-12=144/x

We move all terms to the left:

2x-12-(144/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+144/x)-12=0

We get rid of parentheses

2x-144/x-12=0

We multiply all the terms by the denominator


2x*x-12*x-144=0

We add all the numbers together, and all the variables

-12x+2x*x-144=0

Wy multiply elements

2x^2-12x-144=0

a = 2; b = -12; c = -144;
Δ = b2-4ac
Δ = -122-4·2·(-144)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-36}{2*2}=\frac{-24}{4}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+36}{2*2}=\frac{48}{4}
=12
$