3/4m-2(m-1)=1/4m+5

Solution for 3/4m-2(m-1)=1/4m+5 equation:

3/4m-2(m-1)=1/4m+5

We move all terms to the left:

3/4m-2(m-1)-(1/4m+5)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R



Domain of the equation: 4m+5)!=0

m∈R


We multiply parentheses

3/4m-2m-(1/4m+5)+2=0

We get rid of parentheses

3/4m-2m-1/4m-5+2=0

We multiply all the terms by the denominator


-2m*4m-5*4m+2*4m+3-1=0

We add all the numbers together, and all the variables

-2m*4m-5*4m+2*4m+2=0

Wy multiply elements

-8m^2-20m+8m+2=0

We add all the numbers together, and all the variables

-8m^2-12m+2=0

a = -8; b = -12; c = +2;
Δ = b2-4ac
Δ = -122-4·(-8)·2
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{13}}{2*-8}=\frac{12-4\sqrt{13}}{-16}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{13}}{2*-8}=\frac{12+4\sqrt{13}}{-16}
$