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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(6m(m+1)), so:

6m(m+1)

We multiply parentheses

6m^2+6m

Back to the equation:

-(6m^2+6m)


We add all the numbers together, and all the variables

6m-(6m^2+6m)+2=0

We get rid of parentheses

-6m^2+6m-6m+2=0

We add all the numbers together, and all the variables

-6m^2+2=0

a = -6; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-6)·2
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*-6}=\frac{0-4\sqrt{3}}{-12}
=-\frac{4\sqrt{3}}{-12}
=-\frac{\sqrt{3}}{-3}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*-6}=\frac{0+4\sqrt{3}}{-12}
=\frac{4\sqrt{3}}{-12}
=\frac{\sqrt{3}}{-3}
$