4x(x-16)=-63

Solution for 4x(x-16)=-63 equation:

4x(x-16)=-63

We move all terms to the left:

4x(x-16)-(-63)=0

We add all the numbers together, and all the variables

4x(x-16)+63=0

We multiply parentheses

4x^2-64x+63=0

a = 4; b = -64; c = +63;
Δ = b2-4ac
Δ = -642-4·4·63
Δ = 3088
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3088}=\sqrt{16*193}=\sqrt{16}*\sqrt{193}=4\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-4\sqrt{193}}{2*4}=\frac{64-4\sqrt{193}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+4\sqrt{193}}{2*4}=\frac{64+4\sqrt{193}}{8}
$