2/31x+1=16-x

Solution for 2/31x+1=16-x equation:

2/31x+1=16-x

We move all terms to the left:

2/31x+1-(16-x)=0


Domain of the equation: 31x!=0

x!=0/31

x!=0

x∈R


We add all the numbers together, and all the variables

2/31x-(-1x+16)+1=0

We get rid of parentheses

2/31x+1x-16+1=0

We multiply all the terms by the denominator


1x*31x-16*31x+1*31x+2=0

Wy multiply elements

31x^2-496x+31x+2=0

We add all the numbers together, and all the variables

31x^2-465x+2=0

a = 31; b = -465; c = +2;
Δ = b2-4ac
Δ = -4652-4·31·2
Δ = 215977
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-465)-\sqrt{215977}}{2*31}=\frac{465-\sqrt{215977}}{62}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-465)+\sqrt{215977}}{2*31}=\frac{465+\sqrt{215977}}{62}
$