x+10=255/255x-10

Solution for x+10=255/255x-10 equation:

x+10=255/255x-10

We move all terms to the left:

x+10-(255/255x-10)=0


Domain of the equation: 255x-10)!=0

x∈R


We get rid of parentheses

x-255/255x+10+10=0

We multiply all the terms by the denominator


x*255x+10*255x+10*255x-255=0

Wy multiply elements

255x^2+2550x+2550x-255=0

We add all the numbers together, and all the variables

255x^2+5100x-255=0

a = 255; b = 5100; c = -255;
Δ = b2-4ac
Δ = 51002-4·255·(-255)
Δ = 26270100
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:

$\sqrt{\Delta}=\sqrt{26270100}=\sqrt{260100*101}=\sqrt{260100}*\sqrt{101}=510\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5100)-510\sqrt{101}}{2*255}=\frac{-5100-510\sqrt{101}}{510}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5100)+510\sqrt{101}}{2*255}=\frac{-5100+510\sqrt{101}}{510}
$