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

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

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

We move all terms to the left:

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


Domain of the equation: 2m!=0

m!=0/2

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

5/2m-6/7m+11=0

We calculate fractions


35m/14m^2+(-12m)/14m^2+11=0

We multiply all the terms by the denominator


35m+(-12m)+11*14m^2=0

Wy multiply elements

154m^2+35m+(-12m)=0

We get rid of parentheses

154m^2+35m-12m=0

We add all the numbers together, and all the variables

154m^2+23m=0

a = 154; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·154·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*154}=\frac{-46}{308}
=-23/154
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*154}=\frac{0}{308}
=0
$