-3/x+9=x+21

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

-3/x+9=x+21

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We get rid of parentheses

-3/x-x-21+9=0

We multiply all the terms by the denominator


-x*x-21*x+9*x-3=0

We add all the numbers together, and all the variables

-12x-x*x-3=0

Wy multiply elements

-1x^2-12x-3=0

a = -1; b = -12; c = -3;
Δ = b2-4ac
Δ = -122-4·(-1)·(-3)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{33}}{2*-1}=\frac{12-2\sqrt{33}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{33}}{2*-1}=\frac{12+2\sqrt{33}}{-2}
$