x-(1/15*x)=1000

Solution for x-(1/15*x)=1000 equation:

x-(1/15x)=1000

We move all terms to the left:

x-(1/15x)-(1000)=0


Domain of the equation: 15x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+1/15x)-1000=0

We get rid of parentheses

x-1/15x-1000=0

We multiply all the terms by the denominator


x*15x-1000*15x-1=0

Wy multiply elements

15x^2-15000x-1=0

a = 15; b = -15000; c = -1;
Δ = b2-4ac
Δ = -150002-4·15·(-1)
Δ = 225000060
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:

$\sqrt{\Delta}=\sqrt{225000060}=\sqrt{4*56250015}=\sqrt{4}*\sqrt{56250015}=2\sqrt{56250015}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15000)-2\sqrt{56250015}}{2*15}=\frac{15000-2\sqrt{56250015}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15000)+2\sqrt{56250015}}{2*15}=\frac{15000+2\sqrt{56250015}}{30}
$