1/2m+3/4m=3

Solution for 1/2m+3/4m=3 equation:

1/2m+3/4m=3

We move all terms to the left:

1/2m+3/4m-(3)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R


We calculate fractions


4m/8m^2+6m/8m^2-3=0

We multiply all the terms by the denominator


4m+6m-3*8m^2=0

We add all the numbers together, and all the variables

10m-3*8m^2=0

Wy multiply elements

-24m^2+10m=0

a = -24; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-24)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-24}=\frac{-20}{-48}
=5/12
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-24}=\frac{0}{-48}
=0
$