5/2m+7/m=7

Solution for 5/2m+7/m=7 equation:

5/2m+7/m=7

We move all terms to the left:

5/2m+7/m-(7)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: m!=0

m∈R


We calculate fractions


5m/2m^2+14m/2m^2-7=0

We multiply all the terms by the denominator


5m+14m-7*2m^2=0

We add all the numbers together, and all the variables

19m-7*2m^2=0

Wy multiply elements

-14m^2+19m=0

a = -14; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-14)·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*-14}=\frac{-38}{-28}
=1+5/14
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-14}=\frac{0}{-28}
=0
$