7n^2=-48n+64

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

7n^2=-48n+64

We move all terms to the left:

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

We get rid of parentheses

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