62=2m(6m-1)+4m

Solution for 62=2m(6m-1)+4m equation:

62=2m(6m-1)+4m

We move all terms to the left:

62-(2m(6m-1)+4m)=0


We calculate terms in parentheses: -(2m(6m-1)+4m), so:

2m(6m-1)+4m

We add all the numbers together, and all the variables

4m+2m(6m-1)

We multiply parentheses

12m^2+4m-2m

We add all the numbers together, and all the variables

12m^2+2m

Back to the equation:

-(12m^2+2m)


We get rid of parentheses

-12m^2-2m+62=0

a = -12; b = -2; c = +62;
Δ = b2-4ac
Δ = -22-4·(-12)·62
Δ = 2980
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:

$\sqrt{\Delta}=\sqrt{2980}=\sqrt{4*745}=\sqrt{4}*\sqrt{745}=2\sqrt{745}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{745}}{2*-12}=\frac{2-2\sqrt{745}}{-24}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{745}}{2*-12}=\frac{2+2\sqrt{745}}{-24}
$