x+21-1/3x=9

Solution for x+21-1/3x=9 equation:

x+21-1/3x=9

We move all terms to the left:

x+21-1/3x-(9)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x-1/3x+12=0

We multiply all the terms by the denominator


x*3x+12*3x-1=0

Wy multiply elements

3x^2+36x-1=0

a = 3; b = 36; c = -1;
Δ = b2-4ac
Δ = 362-4·3·(-1)
Δ = 1308
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:

$\sqrt{\Delta}=\sqrt{1308}=\sqrt{4*327}=\sqrt{4}*\sqrt{327}=2\sqrt{327}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{327}}{2*3}=\frac{-36-2\sqrt{327}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{327}}{2*3}=\frac{-36+2\sqrt{327}}{6}
$