X=12-35/y

Solution for X=12-35/y equation:

X=12-35/X

We move all terms to the left:

X-(12-35/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-(-35/X+12)=0

We get rid of parentheses

X+35/X-12=0

We multiply all the terms by the denominator


X*X-12*X+35=0

We add all the numbers together, and all the variables

-12X+X*X+35=0

Wy multiply elements

X^2-12X+35=0

a = 1; b = -12; c = +35;
Δ = b2-4ac
Δ = -122-4·1·35
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2}{2*1}=\frac{10}{2}
=5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2}{2*1}=\frac{14}{2}
=7
$