11/12x-x=-55

Solution for 11/12x-x=-55 equation:

11/12x-x=-55

We move all terms to the left:

11/12x-x-(-55)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+11/12x+55=0

We multiply all the terms by the denominator


-1x*12x+55*12x+11=0

Wy multiply elements

-12x^2+660x+11=0

a = -12; b = 660; c = +11;
Δ = b2-4ac
Δ = 6602-4·(-12)·11
Δ = 436128
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:

$\sqrt{\Delta}=\sqrt{436128}=\sqrt{16*27258}=\sqrt{16}*\sqrt{27258}=4\sqrt{27258}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(660)-4\sqrt{27258}}{2*-12}=\frac{-660-4\sqrt{27258}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(660)+4\sqrt{27258}}{2*-12}=\frac{-660+4\sqrt{27258}}{-24}
$