-6x+36/x=12

Solution for -6x+36/x=12 equation:

-6x+36/x=12

We move all terms to the left:

-6x+36/x-(12)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


-6x*x-12*x+36=0

We add all the numbers together, and all the variables

-12x-6x*x+36=0

Wy multiply elements

-6x^2-12x+36=0

a = -6; b = -12; c = +36;
Δ = b2-4ac
Δ = -122-4·(-6)·36
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{7}}{2*-6}=\frac{12-12\sqrt{7}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{7}}{2*-6}=\frac{12+12\sqrt{7}}{-12}
$