X=10/y+5

Solution for X=10/y+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}
$