60/x-1=36x-1+12

Solution for 60/x-1=36x-1+12 equation:

60/x-1=36x-1+12

We move all terms to the left:

60/x-1-(36x-1+12)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

60/x-(36x+11)-1=0

We get rid of parentheses

60/x-36x-11-1=0

We multiply all the terms by the denominator


-36x*x-11*x-1*x+60=0

We add all the numbers together, and all the variables

-12x-36x*x+60=0

Wy multiply elements

-36x^2-12x+60=0

a = -36; b = -12; c = +60;
Δ = b2-4ac
Δ = -122-4·(-36)·60
Δ = 8784
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:

$\sqrt{\Delta}=\sqrt{8784}=\sqrt{144*61}=\sqrt{144}*\sqrt{61}=12\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{61}}{2*-36}=\frac{12-12\sqrt{61}}{-72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{61}}{2*-36}=\frac{12+12\sqrt{61}}{-72}
$