29/y+y=29

Solution for 29/y+y=29 equation:

29/y+y=29

We move all terms to the left:

29/y+y-(29)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

y+29/y-29=0

We multiply all the terms by the denominator


y*y-29*y+29=0

We add all the numbers together, and all the variables

-29y+y*y+29=0

Wy multiply elements

y^2-29y+29=0

a = 1; b = -29; c = +29;
Δ = b2-4ac
Δ = -292-4·1·29
Δ = 725
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{725}=\sqrt{25*29}=\sqrt{25}*\sqrt{29}=5\sqrt{29}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-5\sqrt{29}}{2*1}=\frac{29-5\sqrt{29}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+5\sqrt{29}}{2*1}=\frac{29+5\sqrt{29}}{2}
$