4/x-6=10+x

Solution for 4/x-6=10+x equation:

4/x-6=10+x

We move all terms to the left:

4/x-6-(10+x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

4/x-(x+10)-6=0

We get rid of parentheses

4/x-x-10-6=0

We multiply all the terms by the denominator


-x*x-10*x-6*x+4=0

We add all the numbers together, and all the variables

-16x-x*x+4=0

Wy multiply elements

-1x^2-16x+4=0

a = -1; b = -16; c = +4;
Δ = b2-4ac
Δ = -162-4·(-1)·4
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{17}}{2*-1}=\frac{16-4\sqrt{17}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{17}}{2*-1}=\frac{16+4\sqrt{17}}{-2}
$