0=4x^2-4x-63

Solution for 0=4x^2-4x-63 equation:

0=4x^2-4x-63

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-4x^2+4x+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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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