6m-m=(5/6)*(6m-10)

Solution for 6m-m=(5/6)*(6m-10) equation:

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

We move all terms to the left:

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


Domain of the equation: 6)(6m-10))!=0

m∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

-((+30m^2+5/6*-10))+5m=0

We multiply all the terms by the denominator


-((+30m^2+5+5m*6*-10))=0


We calculate terms in parentheses: -((+30m^2+5+5m*6*-10)), so:

(+30m^2+5+5m*6*-10)

We get rid of parentheses

30m^2+5m*6*+5-10

We add all the numbers together, and all the variables

30m^2+5m*6*-5

Wy multiply elements

30m^2+30m^2-5

We add all the numbers together, and all the variables

60m^2-5

Back to the equation:

-(60m^2-5)


We get rid of parentheses

-60m^2+5=0

a = -60; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-60)·5
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{3}}{2*-60}=\frac{0-20\sqrt{3}}{-120}
=-\frac{20\sqrt{3}}{-120}
=-\frac{\sqrt{3}}{-6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{3}}{2*-60}=\frac{0+20\sqrt{3}}{-120}
=\frac{20\sqrt{3}}{-120}
=\frac{\sqrt{3}}{-6}
$