8n(6n+7)=7

Solution for 8n(6n+7)=7 equation:

8n(6n+7)=7

We move all terms to the left:

8n(6n+7)-(7)=0

We multiply parentheses

48n^2+56n-7=0

a = 48; b = 56; c = -7;
Δ = b2-4ac
Δ = 562-4·48·(-7)
Δ = 4480
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:

$\sqrt{\Delta}=\sqrt{4480}=\sqrt{64*70}=\sqrt{64}*\sqrt{70}=8\sqrt{70}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-8\sqrt{70}}{2*48}=\frac{-56-8\sqrt{70}}{96}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+8\sqrt{70}}{2*48}=\frac{-56+8\sqrt{70}}{96}
$