6m(2m+9)+5m=(1-3m)

Solution for 6m(2m+9)+5m=(1-3m) equation:

6m(2m+9)+5m=(1-3m)

We move all terms to the left:

6m(2m+9)+5m-((1-3m))=0

We add all the numbers together, and all the variables

6m(2m+9)+5m-((-3m+1))=0

We add all the numbers together, and all the variables

5m+6m(2m+9)-((-3m+1))=0

We multiply parentheses

12m^2+5m+54m-((-3m+1))=0


We calculate terms in parentheses: -((-3m+1)), so:

(-3m+1)

We get rid of parentheses

-3m+1

Back to the equation:

-(-3m+1)


We add all the numbers together, and all the variables

12m^2+59m-(-3m+1)=0

We get rid of parentheses

12m^2+59m+3m-1=0

We add all the numbers together, and all the variables

12m^2+62m-1=0

a = 12; b = 62; c = -1;
Δ = b2-4ac
Δ = 622-4·12·(-1)
Δ = 3892
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:

$\sqrt{\Delta}=\sqrt{3892}=\sqrt{4*973}=\sqrt{4}*\sqrt{973}=2\sqrt{973}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-2\sqrt{973}}{2*12}=\frac{-62-2\sqrt{973}}{24}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+2\sqrt{973}}{2*12}=\frac{-62+2\sqrt{973}}{24}
$