8n(-3n+7)=13

Solution for 8n(-3n+7)=13 equation:

8n(-3n+7)=13

We move all terms to the left:

8n(-3n+7)-(13)=0

We multiply parentheses

-24n^2+56n-13=0

a = -24; b = 56; c = -13;
Δ = b2-4ac
Δ = 562-4·(-24)·(-13)
Δ = 1888
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:

$\sqrt{\Delta}=\sqrt{1888}=\sqrt{16*118}=\sqrt{16}*\sqrt{118}=4\sqrt{118}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-4\sqrt{118}}{2*-24}=\frac{-56-4\sqrt{118}}{-48}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+4\sqrt{118}}{2*-24}=\frac{-56+4\sqrt{118}}{-48}
$