x-31=234/x

Solution for x-31=234/x equation:

x-31=234/x

We move all terms to the left:

x-31-(234/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+234/x)-31=0

We get rid of parentheses

x-234/x-31=0

We multiply all the terms by the denominator


x*x-31*x-234=0

We add all the numbers together, and all the variables

-31x+x*x-234=0

Wy multiply elements

x^2-31x-234=0

a = 1; b = -31; c = -234;
Δ = b2-4ac
Δ = -312-4·1·(-234)
Δ = 1897
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{-(-31)-\sqrt{1897}}{2*1}=\frac{31-\sqrt{1897}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{1897}}{2*1}=\frac{31+\sqrt{1897}}{2}
$