21=m+9/m=11

Solution for 21=m+9/m=11 equation:

21=m+9/m=11

We move all terms to the left:

21-(m+9/m)=0


Domain of the equation: m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

-(+m+9/m)+21=0

We get rid of parentheses

-m-9/m+21=0

We multiply all the terms by the denominator


-m*m+21*m-9=0

We add all the numbers together, and all the variables

21m-m*m-9=0

Wy multiply elements

-1m^2+21m-9=0

a = -1; b = 21; c = -9;
Δ = b2-4ac
Δ = 212-4·(-1)·(-9)
Δ = 405
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{405}=\sqrt{81*5}=\sqrt{81}*\sqrt{5}=9\sqrt{5}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-9\sqrt{5}}{2*-1}=\frac{-21-9\sqrt{5}}{-2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+9\sqrt{5}}{2*-1}=\frac{-21+9\sqrt{5}}{-2}
$