8n(2n+7)=29

Solution for 8n(2n+7)=29 equation:

8n(2n+7)=29

We move all terms to the left:

8n(2n+7)-(29)=0

We multiply parentheses

16n^2+56n-29=0

a = 16; b = 56; c = -29;
Δ = b2-4ac
Δ = 562-4·16·(-29)
Δ = 4992
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:

$\sqrt{\Delta}=\sqrt{4992}=\sqrt{64*78}=\sqrt{64}*\sqrt{78}=8\sqrt{78}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-8\sqrt{78}}{2*16}=\frac{-56-8\sqrt{78}}{32}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+8\sqrt{78}}{2*16}=\frac{-56+8\sqrt{78}}{32}
$