2x-12/x=10/x+6

Solution for 2x-12/x=10/x+6 equation:

2x-12/x=10/x+6

We move all terms to the left:

2x-12/x-(10/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

2x-12/x-10/x-6=0

We multiply all the terms by the denominator


2x*x-6*x-12-10=0

We add all the numbers together, and all the variables

-6x+2x*x-22=0

Wy multiply elements

2x^2-6x-22=0

a = 2; b = -6; c = -22;
Δ = b2-4ac
Δ = -62-4·2·(-22)
Δ = 212
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:

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{53}}{2*2}=\frac{6-2\sqrt{53}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{53}}{2*2}=\frac{6+2\sqrt{53}}{4}
$