(11/29y)+y=44

Solution for (11/29y)+y=44 equation:

(11/29y)+y=44

We move all terms to the left:

(11/29y)+y-(44)=0


Domain of the equation: 29y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(+11/29y)+y-44=0

We add all the numbers together, and all the variables

y+(+11/29y)-44=0

We get rid of parentheses

y+11/29y-44=0

We multiply all the terms by the denominator


y*29y-44*29y+11=0

Wy multiply elements

29y^2-1276y+11=0

a = 29; b = -1276; c = +11;
Δ = b2-4ac
Δ = -12762-4·29·11
Δ = 1626900
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:

$\sqrt{\Delta}=\sqrt{1626900}=\sqrt{100*16269}=\sqrt{100}*\sqrt{16269}=10\sqrt{16269}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1276)-10\sqrt{16269}}{2*29}=\frac{1276-10\sqrt{16269}}{58}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1276)+10\sqrt{16269}}{2*29}=\frac{1276+10\sqrt{16269}}{58}
$