5/11m=m+12

Solution for 5/11m=m+12 equation:

5/11m=m+12

We move all terms to the left:

5/11m-(m+12)=0


Domain of the equation: 11m!=0

m!=0/11

m!=0

m∈R


We get rid of parentheses

5/11m-m-12=0

We multiply all the terms by the denominator


-m*11m-12*11m+5=0

Wy multiply elements

-11m^2-132m+5=0

a = -11; b = -132; c = +5;
Δ = b2-4ac
Δ = -1322-4·(-11)·5
Δ = 17644
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:

$\sqrt{\Delta}=\sqrt{17644}=\sqrt{4*4411}=\sqrt{4}*\sqrt{4411}=2\sqrt{4411}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-2\sqrt{4411}}{2*-11}=\frac{132-2\sqrt{4411}}{-22}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+2\sqrt{4411}}{2*-11}=\frac{132+2\sqrt{4411}}{-22}
$