x=50/x-5

Solution for x=50/x-5 equation:

x=50/x-5

We move all terms to the left:

x-(50/x-5)=0


Domain of the equation: x-5)!=0

x∈R


We get rid of parentheses

x-50/x+5=0

We multiply all the terms by the denominator


x*x+5*x-50=0

We add all the numbers together, and all the variables

5x+x*x-50=0

Wy multiply elements

x^2+5x-50=0

a = 1; b = 5; c = -50;
Δ = b2-4ac
Δ = 52-4·1·(-50)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-15}{2*1}=\frac{-20}{2}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+15}{2*1}=\frac{10}{2}
=5
$