-3/7m+5=3+2m

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

-3/7m+5=3+2m

We move all terms to the left:

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


Domain of the equation: 7m!=0

m!=0/7

m!=0

m∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-3/7m-2m-3+5=0

We multiply all the terms by the denominator


-2m*7m-3*7m+5*7m-3=0

Wy multiply elements

-14m^2-21m+35m-3=0

We add all the numbers together, and all the variables

-14m^2+14m-3=0

a = -14; b = 14; c = -3;
Δ = b2-4ac
Δ = 142-4·(-14)·(-3)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{7}}{2*-14}=\frac{-14-2\sqrt{7}}{-28}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{7}}{2*-14}=\frac{-14+2\sqrt{7}}{-28}
$