-3/4m+5/8m-7/4m+7/8m=-3

Solution for -3/4m+5/8m-7/4m+7/8m=-3 equation:

-3/4m+5/8m-7/4m+7/8m=-3

We move all terms to the left:

-3/4m+5/8m-7/4m+7/8m-(-3)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R



Domain of the equation: 8m!=0

m!=0/8

m!=0

m∈R


We add all the numbers together, and all the variables

-3/4m+5/8m-7/4m+7/8m+3=0

We calculate fractions


(-56m-3)/32m^2+(28m+5)/32m^2+3=0

We multiply all the terms by the denominator


(-56m-3)+(28m+5)+3*32m^2=0

Wy multiply elements

96m^2+(-56m-3)+(28m+5)=0

We get rid of parentheses

96m^2-56m+28m-3+5=0

We add all the numbers together, and all the variables

96m^2-28m+2=0

a = 96; b = -28; c = +2;
Δ = b2-4ac
Δ = -282-4·96·2
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{-(-28)-4}{2*96}=\frac{24}{192}
=1/8
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4}{2*96}=\frac{32}{192}
=1/6
$