X=10/x-5

Solution for X=10/x-5 equation:

X=10/X-5

We move all terms to the left:

X-(10/X-5)=0


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

X∈R


We get rid of parentheses

X-10/X+5=0

We multiply all the terms by the denominator


X*X+5*X-10=0

We add all the numbers together, and all the variables

5X+X*X-10=0

Wy multiply elements

X^2+5X-10=0

a = 1; b = 5; c = -10;
Δ = b2-4ac
Δ = 52-4·1·(-10)
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{65}}{2*1}=\frac{-5-\sqrt{65}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{65}}{2*1}=\frac{-5+\sqrt{65}}{2}
$