1/8m-27=16m=

Solution for 1/8m-27=16m= equation:

1/8m-27=16m=

We move all terms to the left:

1/8m-27-(16m)=0


Domain of the equation: 8m!=0

m!=0/8

m!=0

m∈R


We add all the numbers together, and all the variables

-16m+1/8m-27=0

We multiply all the terms by the denominator


-16m*8m-27*8m+1=0

Wy multiply elements

-128m^2-216m+1=0

a = -128; b = -216; c = +1;
Δ = b2-4ac
Δ = -2162-4·(-128)·1
Δ = 47168
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:

$\sqrt{\Delta}=\sqrt{47168}=\sqrt{64*737}=\sqrt{64}*\sqrt{737}=8\sqrt{737}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-8\sqrt{737}}{2*-128}=\frac{216-8\sqrt{737}}{-256}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+8\sqrt{737}}{2*-128}=\frac{216+8\sqrt{737}}{-256}
$