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

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

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

We move all terms to the left:

5/7m-2-6/5m-(-13)=0


Domain of the equation: 7m!=0

m!=0/7

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

5/7m-6/5m+11=0

We calculate fractions


25m/35m^2+(-42m)/35m^2+11=0

We multiply all the terms by the denominator


25m+(-42m)+11*35m^2=0

Wy multiply elements

385m^2+25m+(-42m)=0

We get rid of parentheses

385m^2+25m-42m=0

We add all the numbers together, and all the variables

385m^2-17m=0

a = 385; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·385·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*385}=\frac{0}{770}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*385}=\frac{34}{770}
=17/385
$