1/3m-1=0.25m+3

Solution for 1/3m-1=0.25m+3 equation:

1/3m-1=0.25m+3

We move all terms to the left:

1/3m-1-(0.25m+3)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We get rid of parentheses

1/3m-0.25m-3-1=0

We multiply all the terms by the denominator


-(0.25m)*3m-3*3m-1*3m+1=0

We add all the numbers together, and all the variables

-(+0.25m)*3m-3*3m-1*3m+1=0

We multiply parentheses

-0m^2-3*3m-1*3m+1=0

Wy multiply elements

-0m^2-9m-3m+1=0

We add all the numbers together, and all the variables

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

a = -1; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·(-1)·1
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{37}}{2*-1}=\frac{12-2\sqrt{37}}{-2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{37}}{2*-1}=\frac{12+2\sqrt{37}}{-2}
$