2/y+y-4=31

Solution for 2/y+y-4=31 equation:

2/y+y-4=31

We move all terms to the left:

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


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

y+2/y-35=0

We multiply all the terms by the denominator


y*y-35*y+2=0

We add all the numbers together, and all the variables

-35y+y*y+2=0

Wy multiply elements

y^2-35y+2=0

a = 1; b = -35; c = +2;
Δ = b2-4ac
Δ = -352-4·1·2
Δ = 1217
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{-(-35)-\sqrt{1217}}{2*1}=\frac{35-\sqrt{1217}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1217}}{2*1}=\frac{35+\sqrt{1217}}{2}
$