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

Solution for 7m-3/5m=6/5m equation:

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

We move all terms to the left:

7m-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

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

We get rid of parentheses

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

We multiply all the terms by the denominator


7m*5m-3-6=0

We add all the numbers together, and all the variables

7m*5m-9=0

Wy multiply elements

35m^2-9=0

a = 35; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·35·(-9)
Δ = 1260
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1260}=\sqrt{36*35}=\sqrt{36}*\sqrt{35}=6\sqrt{35}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{35}}{2*35}=\frac{0-6\sqrt{35}}{70}
=-\frac{6\sqrt{35}}{70}
=-\frac{3\sqrt{35}}{35}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{35}}{2*35}=\frac{0+6\sqrt{35}}{70}
=\frac{6\sqrt{35}}{70}
=\frac{3\sqrt{35}}{35}
$