(273/y)+y=-34

Solution for (273/y)+y=-34 equation:

(273/y)+y=-34

We move all terms to the left:

(273/y)+y-(-34)=0


Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(+273/y)+y-(-34)=0

We add all the numbers together, and all the variables

y+(+273/y)+34=0

We get rid of parentheses

y+273/y+34=0

We multiply all the terms by the denominator


y*y+34*y+273=0

We add all the numbers together, and all the variables

34y+y*y+273=0

Wy multiply elements

y^2+34y+273=0

a = 1; b = 34; c = +273;
Δ = b2-4ac
Δ = 342-4·1·273
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-8}{2*1}=\frac{-42}{2}
=-21
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+8}{2*1}=\frac{-26}{2}
=-13
$