x-6/x=35/x+6

Solution for x-6/x=35/x+6 equation:

x-6/x=35/x+6

We move all terms to the left:

x-6/x-(35/x+6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x+6)!=0

x∈R


We get rid of parentheses

x-6/x-35/x-6=0

We multiply all the terms by the denominator


x*x-6*x-6-35=0

We add all the numbers together, and all the variables

-6x+x*x-41=0

Wy multiply elements

x^2-6x-41=0

a = 1; b = -6; c = -41;
Δ = b2-4ac
Δ = -62-4·1·(-41)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-10\sqrt{2}}{2*1}=\frac{6-10\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+10\sqrt{2}}{2*1}=\frac{6+10\sqrt{2}}{2}
$