3/4m=1+3m

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

3/4m=1+3m

We move all terms to the left:

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


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3/4m-3m-1=0

We multiply all the terms by the denominator


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

Wy multiply elements

-12m^2-4m+3=0

a = -12; b = -4; c = +3;
Δ = b2-4ac
Δ = -42-4·(-12)·3
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{10}}{2*-12}=\frac{4-4\sqrt{10}}{-24}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{10}}{2*-12}=\frac{4+4\sqrt{10}}{-24}
$