2x-1=21/x

Solution for 2x-1=21/x equation:

2x-1=21/x

We move all terms to the left:

2x-1-(21/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

2x-(+21/x)-1=0

We get rid of parentheses

2x-21/x-1=0

We multiply all the terms by the denominator


2x*x-1*x-21=0

We add all the numbers together, and all the variables

-1x+2x*x-21=0

Wy multiply elements

2x^2-1x-21=0

a = 2; b = -1; c = -21;
Δ = b2-4ac
Δ = -12-4·2·(-21)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-13}{2*2}=\frac{-12}{4}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+13}{2*2}=\frac{14}{4}
=3+1/2
$