1/2m+7=16-3/5m

Solution for 1/2m+7=16-3/5m equation:

1/2m+7=16-3/5m

We move all terms to the left:

1/2m+7-(16-3/5m)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: 5m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

1/2m-(-3/5m+16)+7=0

We get rid of parentheses

1/2m+3/5m-16+7=0

We calculate fractions


5m/10m^2+6m/10m^2-16+7=0

We add all the numbers together, and all the variables

5m/10m^2+6m/10m^2-9=0

We multiply all the terms by the denominator


5m+6m-9*10m^2=0

We add all the numbers together, and all the variables

11m-9*10m^2=0

Wy multiply elements

-90m^2+11m=0

a = -90; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-90)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-90}=\frac{-22}{-180}
=11/90
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-90}=\frac{0}{-180}
=0
$