16m-1/10m=4

Solution for 16m-1/10m=4 equation:

16m-1/10m=4

We move all terms to the left:

16m-1/10m-(4)=0


Domain of the equation: 10m!=0

m!=0/10

m!=0

m∈R


We multiply all the terms by the denominator


16m*10m-4*10m-1=0

Wy multiply elements

160m^2-40m-1=0

a = 160; b = -40; c = -1;
Δ = b2-4ac
Δ = -402-4·160·(-1)
Δ = 2240
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:

$\sqrt{\Delta}=\sqrt{2240}=\sqrt{64*35}=\sqrt{64}*\sqrt{35}=8\sqrt{35}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{35}}{2*160}=\frac{40-8\sqrt{35}}{320}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{35}}{2*160}=\frac{40+8\sqrt{35}}{320}
$