1/4m+3=8m

Solution for 1/4m+3=8m equation:

1/4m+3=8m

We move all terms to the left:

1/4m+3-(8m)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R


We add all the numbers together, and all the variables

-8m+1/4m+3=0

We multiply all the terms by the denominator


-8m*4m+3*4m+1=0

Wy multiply elements

-32m^2+12m+1=0

a = -32; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·(-32)·1
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{17}}{2*-32}=\frac{-12-4\sqrt{17}}{-64}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{17}}{2*-32}=\frac{-12+4\sqrt{17}}{-64}
$