3x+6/x-5=5

Solution for 3x+6/x-5=5 equation:

3x+6/x-5=5

We move all terms to the left:

3x+6/x-5-(5)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x+6/x-10=0

We multiply all the terms by the denominator


3x*x-10*x+6=0

We add all the numbers together, and all the variables

-10x+3x*x+6=0

Wy multiply elements

3x^2-10x+6=0

a = 3; b = -10; c = +6;
Δ = b2-4ac
Δ = -102-4·3·6
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{7}}{2*3}=\frac{10-2\sqrt{7}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{7}}{2*3}=\frac{10+2\sqrt{7}}{6}
$