x-1/11x=5000

Solution for x-1/11x=5000 equation:

x-1/11x=5000

We move all terms to the left:

x-1/11x-(5000)=0


Domain of the equation: 11x!=0

x!=0/11

x!=0

x∈R


We multiply all the terms by the denominator


x*11x-5000*11x-1=0

Wy multiply elements

11x^2-55000x-1=0

a = 11; b = -55000; c = -1;
Δ = b2-4ac
Δ = -550002-4·11·(-1)
Δ = 3025000044
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:

$\sqrt{\Delta}=\sqrt{3025000044}=\sqrt{36*84027779}=\sqrt{36}*\sqrt{84027779}=6\sqrt{84027779}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55000)-6\sqrt{84027779}}{2*11}=\frac{55000-6\sqrt{84027779}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55000)+6\sqrt{84027779}}{2*11}=\frac{55000+6\sqrt{84027779}}{22}
$