7n(-6n+3)-2=-107

Solution for 7n(-6n+3)-2=-107 equation:

7n(-6n+3)-2=-107

We move all terms to the left:

7n(-6n+3)-2-(-107)=0

We add all the numbers together, and all the variables

7n(-6n+3)+105=0

We multiply parentheses

-42n^2+21n+105=0

a = -42; b = 21; c = +105;
Δ = b2-4ac
Δ = 212-4·(-42)·105
Δ = 18081
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:

$\sqrt{\Delta}=\sqrt{18081}=\sqrt{441*41}=\sqrt{441}*\sqrt{41}=21\sqrt{41}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21\sqrt{41}}{2*-42}=\frac{-21-21\sqrt{41}}{-84}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21\sqrt{41}}{2*-42}=\frac{-21+21\sqrt{41}}{-84}
$