4/7y+y=31

Solution for 4/7y+y=31 equation:

4/7y+y=31

We move all terms to the left:

4/7y+y-(31)=0


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R


We add all the numbers together, and all the variables

y+4/7y-31=0

We multiply all the terms by the denominator


y*7y-31*7y+4=0

Wy multiply elements

7y^2-217y+4=0

a = 7; b = -217; c = +4;
Δ = b2-4ac
Δ = -2172-4·7·4
Δ = 46977
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-217)-\sqrt{46977}}{2*7}=\frac{217-\sqrt{46977}}{14}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-217)+\sqrt{46977}}{2*7}=\frac{217+\sqrt{46977}}{14}
$