2+1/3m+3/10m+7=5

Solution for 2+1/3m+3/10m+7=5 equation:

2+1/3m+3/10m+7=5

We move all terms to the left:

2+1/3m+3/10m+7-(5)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: 10m!=0

m!=0/10

m!=0

m∈R


We add all the numbers together, and all the variables

1/3m+3/10m+4=0

We calculate fractions


10m/30m^2+9m/30m^2+4=0

We multiply all the terms by the denominator


10m+9m+4*30m^2=0

We add all the numbers together, and all the variables

19m+4*30m^2=0

Wy multiply elements

120m^2+19m=0

a = 120; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·120·0
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*120}=\frac{-38}{240}
=-19/120
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*120}=\frac{0}{240}
=0
$