8(-2n-7)2n=-146

Solution for 8(-2n-7)2n=-146 equation:

8(-2n-7)2n=-146

We move all terms to the left:

8(-2n-7)2n-(-146)=0

We add all the numbers together, and all the variables

8(-2n-7)2n+146=0

We multiply parentheses

-32n^2-112n+146=0

a = -32; b = -112; c = +146;
Δ = b2-4ac
Δ = -1122-4·(-32)·146
Δ = 31232
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:

$\sqrt{\Delta}=\sqrt{31232}=\sqrt{256*122}=\sqrt{256}*\sqrt{122}=16\sqrt{122}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-16\sqrt{122}}{2*-32}=\frac{112-16\sqrt{122}}{-64}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+16\sqrt{122}}{2*-32}=\frac{112+16\sqrt{122}}{-64}
$