3/4m-1/8m-6=15

Solution for 3/4m-1/8m-6=15 equation:

3/4m-1/8m-6=15

We move all terms to the left:

3/4m-1/8m-6-(15)=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-1/8m-21=0

We calculate fractions


24m/32m^2+(-4m)/32m^2-21=0

We multiply all the terms by the denominator


24m+(-4m)-21*32m^2=0

Wy multiply elements

-672m^2+24m+(-4m)=0

We get rid of parentheses

-672m^2+24m-4m=0

We add all the numbers together, and all the variables

-672m^2+20m=0

a = -672; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-672)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-672}=\frac{-40}{-1344}
=5/168
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-672}=\frac{0}{-1344}
=0
$