0=6n^2-4n-1092

Solution for 0=6n^2-4n-1092 equation:

0=6n^2-4n-1092

We move all terms to the left:

0-(6n^2-4n-1092)=0

We add all the numbers together, and all the variables

-(6n^2-4n-1092)=0

We get rid of parentheses

-6n^2+4n+1092=0

a = -6; b = 4; c = +1092;
Δ = b2-4ac
Δ = 42-4·(-6)·1092
Δ = 26224
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:

$\sqrt{\Delta}=\sqrt{26224}=\sqrt{16*1639}=\sqrt{16}*\sqrt{1639}=4\sqrt{1639}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{1639}}{2*-6}=\frac{-4-4\sqrt{1639}}{-12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{1639}}{2*-6}=\frac{-4+4\sqrt{1639}}{-12}
$