x-1/10x=360

Solution for x-1/10x=360 equation:

x-1/10x=360

We move all terms to the left:

x-1/10x-(360)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We multiply all the terms by the denominator


x*10x-360*10x-1=0

Wy multiply elements

10x^2-3600x-1=0

a = 10; b = -3600; c = -1;
Δ = b2-4ac
Δ = -36002-4·10·(-1)
Δ = 12960040
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:

$\sqrt{\Delta}=\sqrt{12960040}=\sqrt{4*3240010}=\sqrt{4}*\sqrt{3240010}=2\sqrt{3240010}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3600)-2\sqrt{3240010}}{2*10}=\frac{3600-2\sqrt{3240010}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3600)+2\sqrt{3240010}}{2*10}=\frac{3600+2\sqrt{3240010}}{20}
$