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

Solution for m/2m-7=-5m+14 equation:

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

We move all terms to the left:

m/2m-7-(-5m+14)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

10m^2+m-28m-14m=0

We add all the numbers together, and all the variables

10m^2-41m=0

a = 10; b = -41; c = 0;
Δ = b2-4ac
Δ = -412-4·10·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-41}{2*10}=\frac{0}{20}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+41}{2*10}=\frac{82}{20}
=4+1/10
$