(21x-21/x+1)-4=2x

Solution for (21x-21/x+1)-4=2x equation:

(21x-21/x+1)-4=2x

We move all terms to the left:

(21x-21/x+1)-4-(2x)=0


Domain of the equation: x+1)!=0

x∈R


We add all the numbers together, and all the variables

-2x+(21x-21/x+1)-4=0

We get rid of parentheses

-2x+21x-21/x+1-4=0

We multiply all the terms by the denominator


-2x*x+21x*x+1*x-4*x-21=0

We add all the numbers together, and all the variables

-3x-2x*x+21x*x-21=0

Wy multiply elements

-2x^2+21x^2-3x-21=0

We add all the numbers together, and all the variables

19x^2-3x-21=0

a = 19; b = -3; c = -21;
Δ = b2-4ac
Δ = -32-4·19·(-21)
Δ = 1605
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{-(-3)-\sqrt{1605}}{2*19}=\frac{3-\sqrt{1605}}{38}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{1605}}{2*19}=\frac{3+\sqrt{1605}}{38}
$