X-(1/10x)=10

Solution for X-(1/10x)=10 equation:

X-(1/10X)=10

We move all terms to the left:

X-(1/10X)-(10)=0


Domain of the equation: 10X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(+1/10X)-10=0

We get rid of parentheses

X-1/10X-10=0

We multiply all the terms by the denominator


X*10X-10*10X-1=0

Wy multiply elements

10X^2-100X-1=0

a = 10; b = -100; c = -1;
Δ = b2-4ac
Δ = -1002-4·10·(-1)
Δ = 10040
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:

$\sqrt{\Delta}=\sqrt{10040}=\sqrt{4*2510}=\sqrt{4}*\sqrt{2510}=2\sqrt{2510}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-2\sqrt{2510}}{2*10}=\frac{100-2\sqrt{2510}}{20}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+2\sqrt{2510}}{2*10}=\frac{100+2\sqrt{2510}}{20}
$