-12=100x-59/x

Solution for -12=100x-59/x equation:

-12=100x-59/x

We move all terms to the left:

-12-(100x-59/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

-(+100x-59/x)-12=0

We get rid of parentheses

-100x+59/x-12=0

We multiply all the terms by the denominator


-100x*x-12*x+59=0

We add all the numbers together, and all the variables

-12x-100x*x+59=0

Wy multiply elements

-100x^2-12x+59=0

a = -100; b = -12; c = +59;
Δ = b2-4ac
Δ = -122-4·(-100)·59
Δ = 23744
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:

$\sqrt{\Delta}=\sqrt{23744}=\sqrt{64*371}=\sqrt{64}*\sqrt{371}=8\sqrt{371}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{371}}{2*-100}=\frac{12-8\sqrt{371}}{-200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{371}}{2*-100}=\frac{12+8\sqrt{371}}{-200}
$