80=2(n+6)n+46

Solution for 80=2(n+6)n+46 equation:

80=2(n+6)n+46

We move all terms to the left:

80-(2(n+6)n+46)=0


We calculate terms in parentheses: -(2(n+6)n+46), so:

2(n+6)n+46

We multiply parentheses

2n^2+12n+46

Back to the equation:

-(2n^2+12n+46)


We get rid of parentheses

-2n^2-12n-46+80=0

We add all the numbers together, and all the variables

-2n^2-12n+34=0

a = -2; b = -12; c = +34;
Δ = b2-4ac
Δ = -122-4·(-2)·34
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{26}}{2*-2}=\frac{12-4\sqrt{26}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{26}}{2*-2}=\frac{12+4\sqrt{26}}{-4}
$