-7n^2-48n+64=0

Solution for -7n^2-48n+64=0 equation:

-7n^2-48n+64=0

a = -7; b = -48; c = +64;
Δ = b2-4ac
Δ = -482-4·(-7)·64
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-64}{2*-7}=\frac{-16}{-14}
=1+1/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+64}{2*-7}=\frac{112}{-14}
=-8
$