365/10x=x

Solution for 365/10x=x equation:

365/10x=x

We move all terms to the left:

365/10x-(x)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+365/10x=0

We multiply all the terms by the denominator


-1x*10x+365=0

Wy multiply elements

-10x^2+365=0

a = -10; b = 0; c = +365;
Δ = b2-4ac
Δ = 02-4·(-10)·365
Δ = 14600
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:

$\sqrt{\Delta}=\sqrt{14600}=\sqrt{100*146}=\sqrt{100}*\sqrt{146}=10\sqrt{146}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{146}}{2*-10}=\frac{0-10\sqrt{146}}{-20}
=-\frac{10\sqrt{146}}{-20}
=-\frac{\sqrt{146}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{146}}{2*-10}=\frac{0+10\sqrt{146}}{-20}
=\frac{10\sqrt{146}}{-20}
=\frac{\sqrt{146}}{-2}
$