6n*(3/6)=40*6

Solution for 6n*(3/6)=40*6 equation:

6n(3/6)=40*6

We move all terms to the left:

6n(3/6)-(40*6)=0

We add all the numbers together, and all the variables

6n(+3/6)-240=0

We multiply parentheses

18n^2-240=0

a = 18; b = 0; c = -240;
Δ = b2-4ac
Δ = 02-4·18·(-240)
Δ = 17280
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{17280}=\sqrt{576*30}=\sqrt{576}*\sqrt{30}=24\sqrt{30}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{30}}{2*18}=\frac{0-24\sqrt{30}}{36}
=-\frac{24\sqrt{30}}{36}
=-\frac{2\sqrt{30}}{3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{30}}{2*18}=\frac{0+24\sqrt{30}}{36}
=\frac{24\sqrt{30}}{36}
=\frac{2\sqrt{30}}{3}
$