3/4m-2/5m=-7

Solution for 3/4m-2/5m=-7 equation:

3/4m-2/5m=-7

We move all terms to the left:

3/4m-2/5m-(-7)=0


Domain of the equation: 4m!=0

m!=0/4

m!=0

m∈R



Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R


We add all the numbers together, and all the variables

3/4m-2/5m+7=0

We calculate fractions


15m/20m^2+(-8m)/20m^2+7=0

We multiply all the terms by the denominator


15m+(-8m)+7*20m^2=0

Wy multiply elements

140m^2+15m+(-8m)=0

We get rid of parentheses

140m^2+15m-8m=0

We add all the numbers together, and all the variables

140m^2+7m=0

a = 140; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·140·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*140}=\frac{-14}{280}
=-1/20
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*140}=\frac{0}{280}
=0
$