x+6/x-15=5

Solution for x+6/x-15=5 equation:

x+6/x-15=5

We move all terms to the left:

x+6/x-15-(5)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+6/x-20=0

We multiply all the terms by the denominator


x*x-20*x+6=0

We add all the numbers together, and all the variables

-20x+x*x+6=0

Wy multiply elements

x^2-20x+6=0

a = 1; b = -20; c = +6;
Δ = b2-4ac
Δ = -202-4·1·6
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{94}}{2*1}=\frac{20-2\sqrt{94}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{94}}{2*1}=\frac{20+2\sqrt{94}}{2}
$