8n(-6n-5)=7

Solution for 8n(-6n-5)=7 equation:

8n(-6n-5)=7

We move all terms to the left:

8n(-6n-5)-(7)=0

We multiply parentheses

-48n^2-40n-7=0

a = -48; b = -40; c = -7;
Δ = b2-4ac
Δ = -402-4·(-48)·(-7)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-16}{2*-48}=\frac{24}{-96}
=-1/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+16}{2*-48}=\frac{56}{-96}
=-7/12
$