x=50+6-x+80/x

Solution for x=50+6-x+80/x equation:

x=50+6-x+80/x

We move all terms to the left:

x-(50+6-x+80/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(-1x+80/x+56)=0

We get rid of parentheses

x+1x-80/x-56=0

We multiply all the terms by the denominator


x*x+1x*x-56*x-80=0

We add all the numbers together, and all the variables

-56x+x*x+1x*x-80=0

Wy multiply elements

x^2+x^2-56x-80=0

We add all the numbers together, and all the variables

2x^2-56x-80=0

a = 2; b = -56; c = -80;
Δ = b2-4ac
Δ = -562-4·2·(-80)
Δ = 3776
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:

$\sqrt{\Delta}=\sqrt{3776}=\sqrt{64*59}=\sqrt{64}*\sqrt{59}=8\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-8\sqrt{59}}{2*2}=\frac{56-8\sqrt{59}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+8\sqrt{59}}{2*2}=\frac{56+8\sqrt{59}}{4}
$