7/8m-1/2=3/12m+5

Solution for 7/8m-1/2=3/12m+5 equation:

7/8m-1/2=3/12m+5

We move all terms to the left:

7/8m-1/2-(3/12m+5)=0


Domain of the equation: 8m!=0

m!=0/8

m!=0

m∈R



Domain of the equation: 12m+5)!=0

m∈R


We get rid of parentheses

7/8m-3/12m-5-1/2=0

We calculate fractions


(-96m^2)/384m^2+336m/384m^2+(-96m)/384m^2-5=0

We multiply all the terms by the denominator


(-96m^2)+336m+(-96m)-5*384m^2=0

Wy multiply elements

(-96m^2)-1920m^2+336m+(-96m)=0

We get rid of parentheses

-96m^2-1920m^2+336m-96m=0

We add all the numbers together, and all the variables

-2016m^2+240m=0

a = -2016; b = 240; c = 0;
Δ = b2-4ac
Δ = 2402-4·(-2016)·0
Δ = 57600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57600}=240$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-240}{2*-2016}=\frac{-480}{-4032}
=5/42
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+240}{2*-2016}=\frac{0}{-4032}
=0
$