3/4m-5/8m=6

Solution for 3/4m-5/8m=6 equation:

3/4m-5/8m=6

We move all terms to the left:

3/4m-5/8m-(6)=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 calculate fractions


24m/32m^2+(-20m)/32m^2-6=0

We multiply all the terms by the denominator


24m+(-20m)-6*32m^2=0

Wy multiply elements

-192m^2+24m+(-20m)=0

We get rid of parentheses

-192m^2+24m-20m=0

We add all the numbers together, and all the variables

-192m^2+4m=0

a = -192; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-192)·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*-192}=\frac{-8}{-384}
=1/48
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-192}=\frac{0}{-384}
=0
$