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

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

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

We move all terms to the left:

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


Domain of the equation: 5m!=0

m!=0/5

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

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

We calculate fractions


49m/35m^2+(-30m)/35m^2+11=0

We multiply all the terms by the denominator


49m+(-30m)+11*35m^2=0

Wy multiply elements

385m^2+49m+(-30m)=0

We get rid of parentheses

385m^2+49m-30m=0

We add all the numbers together, and all the variables

385m^2+19m=0

a = 385; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·385·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*385}=\frac{-38}{770}
=-19/385
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*385}=\frac{0}{770}
=0
$