X+5=1/23x

Solution for X+5=1/23x equation:

X+5=1/23X

We move all terms to the left:

X+5-(1/23X)=0


Domain of the equation: 23X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(+1/23X)+5=0

We get rid of parentheses

X-1/23X+5=0

We multiply all the terms by the denominator


X*23X+5*23X-1=0

Wy multiply elements

23X^2+115X-1=0

a = 23; b = 115; c = -1;
Δ = b2-4ac
Δ = 1152-4·23·(-1)
Δ = 13317
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{-(115)-\sqrt{13317}}{2*23}=\frac{-115-\sqrt{13317}}{46}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(115)+\sqrt{13317}}{2*23}=\frac{-115+\sqrt{13317}}{46}
$