7(2m-1)-3/5m=6/5m=6/5(4-3m)

Solution for 7(2m-1)-3/5m=6/5m=6/5(4-3m) equation:

7(2m-1)-3/5m=6/5m=6/5(4-3m)

We move all terms to the left:

7(2m-1)-3/5m-(6/5m)=0


Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R



Domain of the equation: 5m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

7(2m-1)-3/5m-(+6/5m)=0

We multiply parentheses

14m-3/5m-(+6/5m)-7=0

We get rid of parentheses

14m-3/5m-6/5m-7=0

We multiply all the terms by the denominator


14m*5m-7*5m-3-6=0

We add all the numbers together, and all the variables

14m*5m-7*5m-9=0

Wy multiply elements

70m^2-35m-9=0

a = 70; b = -35; c = -9;
Δ = b2-4ac
Δ = -352-4·70·(-9)
Δ = 3745
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-\sqrt{3745}}{2*70}=\frac{35-\sqrt{3745}}{140}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{3745}}{2*70}=\frac{35+\sqrt{3745}}{140}
$