6m-m=5/66m-10

Solution for 6m-m=5/66m-10 equation:

6m-m=5/66m-10

We move all terms to the left:

6m-m-(5/66m-10)=0


Domain of the equation: 66m-10)!=0

m∈R


We add all the numbers together, and all the variables

5m-(5/66m-10)=0

We get rid of parentheses

5m-5/66m+10=0

We multiply all the terms by the denominator


5m*66m+10*66m-5=0

Wy multiply elements

330m^2+660m-5=0

a = 330; b = 660; c = -5;
Δ = b2-4ac
Δ = 6602-4·330·(-5)
Δ = 442200
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:

$\sqrt{\Delta}=\sqrt{442200}=\sqrt{100*4422}=\sqrt{100}*\sqrt{4422}=10\sqrt{4422}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(660)-10\sqrt{4422}}{2*330}=\frac{-660-10\sqrt{4422}}{660}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(660)+10\sqrt{4422}}{2*330}=\frac{-660+10\sqrt{4422}}{660}
$