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

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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 $

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