3m+1=6m(-2-3m)

Solution for 3m+1=6m(-2-3m) equation:

3m+1=6m(-2-3m)

We move all terms to the left:

3m+1-(6m(-2-3m))=0

We add all the numbers together, and all the variables

3m-(6m(-3m-2))+1=0


We calculate terms in parentheses: -(6m(-3m-2)), so:

6m(-3m-2)

We multiply parentheses

-18m^2-12m

Back to the equation:

-(-18m^2-12m)


We get rid of parentheses

18m^2+12m+3m+1=0

We add all the numbers together, and all the variables

18m^2+15m+1=0

a = 18; b = 15; c = +1;
Δ = b2-4ac
Δ = 152-4·18·1
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{17}}{2*18}=\frac{-15-3\sqrt{17}}{36}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{17}}{2*18}=\frac{-15+3\sqrt{17}}{36}
$