4-3/5m=6-5m+2

Solution for 4-3/5m=6-5m+2 equation:

4-3/5m=6-5m+2

We move all terms to the left:

4-3/5m-(6-5m+2)=0


Domain of the equation: 5m!=0

m!=0/5

m!=0

m∈R


We add all the numbers together, and all the variables

-3/5m-(-5m+8)+4=0

We get rid of parentheses

-3/5m+5m-8+4=0

We multiply all the terms by the denominator


5m*5m-8*5m+4*5m-3=0

Wy multiply elements

25m^2-40m+20m-3=0

We add all the numbers together, and all the variables

25m^2-20m-3=0

a = 25; b = -20; c = -3;
Δ = b2-4ac
Δ = -202-4·25·(-3)
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-10\sqrt{7}}{2*25}=\frac{20-10\sqrt{7}}{50}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+10\sqrt{7}}{2*25}=\frac{20+10\sqrt{7}}{50}
$