3/4m-10=-1/2m-4

Solution for 3/4m-10=-1/2m-4 equation:

3/4m-10=-1/2m-4

We move all terms to the left:

3/4m-10-(-1/2m-4)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R



Domain of the equation: 2m-4)!=0

m∈R


We get rid of parentheses

3/4m+1/2m+4-10=0

We calculate fractions


6m/8m^2+4m/8m^2+4-10=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

10m-6*8m^2=0

Wy multiply elements

-48m^2+10m=0

a = -48; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-48)·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*-48}=\frac{-20}{-96}
=5/24
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-48}=\frac{0}{-96}
=0
$