x-(1/10x)=27

Solution for x-(1/10x)=27 equation:

x-(1/10x)=27

We move all terms to the left:

x-(1/10x)-(27)=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)-27=0

We get rid of parentheses

x-1/10x-27=0

We multiply all the terms by the denominator


x*10x-27*10x-1=0

Wy multiply elements

10x^2-270x-1=0

a = 10; b = -270; c = -1;
Δ = b2-4ac
Δ = -2702-4·10·(-1)
Δ = 72940
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:

$\sqrt{\Delta}=\sqrt{72940}=\sqrt{4*18235}=\sqrt{4}*\sqrt{18235}=2\sqrt{18235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-2\sqrt{18235}}{2*10}=\frac{270-2\sqrt{18235}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+2\sqrt{18235}}{2*10}=\frac{270+2\sqrt{18235}}{20}
$