2-7(6n+9)n=2

Solution for 2-7(6n+9)n=2 equation:

2-7(6n+9)n=2

We move all terms to the left:

2-7(6n+9)n-(2)=0

We add all the numbers together, and all the variables

-7(6n+9)n=0

We multiply parentheses

-42n^2-63n=0

a = -42; b = -63; c = 0;
Δ = b2-4ac
Δ = -632-4·(-42)·0
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-63}{2*-42}=\frac{0}{-84}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+63}{2*-42}=\frac{126}{-84}
=-1+1/2
$