7/2m+4/5m=4

Solution for 7/2m+4/5m=4 equation:

7/2m+4/5m=4

We move all terms to the left:

7/2m+4/5m-(4)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R


We calculate fractions


35m/10m^2+8m/10m^2-4=0

We multiply all the terms by the denominator


35m+8m-4*10m^2=0

We add all the numbers together, and all the variables

43m-4*10m^2=0

Wy multiply elements

-40m^2+43m=0

a = -40; b = 43; c = 0;
Δ = b2-4ac
Δ = 432-4·(-40)·0
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-43}{2*-40}=\frac{-86}{-80}
=1+3/40
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+43}{2*-40}=\frac{0}{-80}
=0
$