-4n^2=4n-63

Solution for -4n^2=4n-63 equation:

-4n^2=4n-63

We move all terms to the left:

-4n^2-(4n-63)=0

We get rid of parentheses

-4n^2-4n+63=0

a = -4; b = -4; c = +63;
Δ = b2-4ac
Δ = -42-4·(-4)·63
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-32}{2*-4}=\frac{-28}{-8}
=3+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+32}{2*-4}=\frac{36}{-8}
=-4+1/2
$