63=z(z-2)

Solution for 63=z(z-2) equation:

63=z(z-2)

We move all terms to the left:

63-(z(z-2))=0


We calculate terms in parentheses: -(z(z-2)), so:

z(z-2)

We multiply parentheses

z^2-2z

Back to the equation:

-(z^2-2z)


We get rid of parentheses

-z^2+2z+63=0

We add all the numbers together, and all the variables

-1z^2+2z+63=0

a = -1; b = 2; c = +63;
Δ = b2-4ac
Δ = 22-4·(-1)·63
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-16}{2*-1}=\frac{-18}{-2}
=+9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+16}{2*-1}=\frac{14}{-2}
=-7
$