2n^2-14n-164=28-6n

Solution for 2n^2-14n-164=28-6n equation:

2n^2-14n-164=28-6n

We move all terms to the left:

2n^2-14n-164-(28-6n)=0

We add all the numbers together, and all the variables

2n^2-14n-(-6n+28)-164=0

We get rid of parentheses

2n^2-14n+6n-28-164=0

We add all the numbers together, and all the variables

2n^2-8n-192=0

a = 2; b = -8; c = -192;
Δ = b2-4ac
Δ = -82-4·2·(-192)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-40}{2*2}=\frac{-32}{4}
=-8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+40}{2*2}=\frac{48}{4}
=12
$