# 5/7m*2-6/7m=-13

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## Solution for 5/7m*2-6/7m=-13 equation:

5/7m*2-6/7m=-13
We move all terms to the left:
5/7m*2-6/7m-(-13)=0

Domain of the equation: 7m*2!=0
m!=0/1
m!=0
m∈R

Domain of the equation: 7m!=0
m!=0/7
m!=0
m∈R

We add all the numbers together, and all the variables
5/7m*2-6/7m+13=0
We calculate fractions

35m/686m^2+(-168m)/686m^2+13=0
We multiply all the terms by the denominator

35m+(-168m)+13*686m^2=0
Wy multiply elements
8918m^2+35m+(-168m)=0
We get rid of parentheses
8918m^2+35m-168m=0
We add all the numbers together, and all the variables
8918m^2-133m=0
a = 8918; b = -133; c = 0;Δ = b2-4acΔ = -1332-4·8918·0Δ = 17689The delta value is higher than zero, so the equation has two solutionsWe use following formulas to calculate our solutions:$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{17689}=133$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-133)-133}{2*8918}=\frac{0}{17836} =0$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-133)+133}{2*8918}=\frac{266}{17836} =19/1274$

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