2n(4n+8)=76

Solution for 2n(4n+8)=76 equation:

2n(4n+8)=76

We move all terms to the left:

2n(4n+8)-(76)=0

We multiply parentheses

8n^2+16n-76=0

a = 8; b = 16; c = -76;
Δ = b2-4ac
Δ = 162-4·8·(-76)
Δ = 2688
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:

$\sqrt{\Delta}=\sqrt{2688}=\sqrt{64*42}=\sqrt{64}*\sqrt{42}=8\sqrt{42}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8\sqrt{42}}{2*8}=\frac{-16-8\sqrt{42}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8\sqrt{42}}{2*8}=\frac{-16+8\sqrt{42}}{16}
$