m+16/m=10

Solution for m+16/m=10 equation:

m+16/m=10

We move all terms to the left:

m+16/m-(10)=0


Domain of the equation: m!=0

m∈R


We multiply all the terms by the denominator


m*m-10*m+16=0

We add all the numbers together, and all the variables

-10m+m*m+16=0

Wy multiply elements

m^2-10m+16=0

a = 1; b = -10; c = +16;
Δ = b2-4ac
Δ = -102-4·1·16
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6}{2*1}=\frac{4}{2}
=2
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6}{2*1}=\frac{16}{2}
=8
$