21x+3/x=21

Solution for 21x+3/x=21 equation:

21x+3/x=21

We move all terms to the left:

21x+3/x-(21)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

21x^2-21x+3=0

a = 21; b = -21; c = +3;
Δ = b2-4ac
Δ = -212-4·21·3
Δ = 189
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{21}}{2*21}=\frac{21-3\sqrt{21}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{21}}{2*21}=\frac{21+3\sqrt{21}}{42}
$