x-(11/12x)=1000

Solution for x-(11/12x)=1000 equation:

x-(11/12x)=1000

We move all terms to the left:

x-(11/12x)-(1000)=0


Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+11/12x)-1000=0

We get rid of parentheses

x-11/12x-1000=0

We multiply all the terms by the denominator


x*12x-1000*12x-11=0

Wy multiply elements

12x^2-12000x-11=0

a = 12; b = -12000; c = -11;
Δ = b2-4ac
Δ = -120002-4·12·(-11)
Δ = 144000528
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:

$\sqrt{\Delta}=\sqrt{144000528}=\sqrt{16*9000033}=\sqrt{16}*\sqrt{9000033}=4\sqrt{9000033}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12000)-4\sqrt{9000033}}{2*12}=\frac{12000-4\sqrt{9000033}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12000)+4\sqrt{9000033}}{2*12}=\frac{12000+4\sqrt{9000033}}{24}
$