1/4m=12-m

Solution for 1/4m=12-m equation:

1/4m=12-m

We move all terms to the left:

1/4m-(12-m)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R


We add all the numbers together, and all the variables

1/4m-(-1m+12)=0

We get rid of parentheses

1/4m+1m-12=0

We multiply all the terms by the denominator


1m*4m-12*4m+1=0

Wy multiply elements

4m^2-48m+1=0

a = 4; b = -48; c = +1;
Δ = b2-4ac
Δ = -482-4·4·1
Δ = 2288
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:

$\sqrt{\Delta}=\sqrt{2288}=\sqrt{16*143}=\sqrt{16}*\sqrt{143}=4\sqrt{143}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{143}}{2*4}=\frac{48-4\sqrt{143}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{143}}{2*4}=\frac{48+4\sqrt{143}}{8}
$