3/4m-1=7/8m+4

Solution for 3/4m-1=7/8m+4 equation:

3/4m-1=7/8m+4

We move all terms to the left:

3/4m-1-(7/8m+4)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R



Domain of the equation: 8m+4)!=0

m∈R


We get rid of parentheses

3/4m-7/8m-4-1=0

We calculate fractions


24m/32m^2+(-28m)/32m^2-4-1=0

We add all the numbers together, and all the variables

24m/32m^2+(-28m)/32m^2-5=0

We multiply all the terms by the denominator


24m+(-28m)-5*32m^2=0

Wy multiply elements

-160m^2+24m+(-28m)=0

We get rid of parentheses

-160m^2+24m-28m=0

We add all the numbers together, and all the variables

-160m^2-4m=0

a = -160; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-160)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-160}=\frac{0}{-320}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-160}=\frac{8}{-320}
=-1/40
$