20x-x^2=63

Solution for 20x-x^2=63 equation:

20x-x^2=63

We move all terms to the left:

20x-x^2-(63)=0

We add all the numbers together, and all the variables

-1x^2+20x-63=0

a = -1; b = 20; c = -63;
Δ = b2-4ac
Δ = 202-4·(-1)·(-63)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{37}}{2*-1}=\frac{-20-2\sqrt{37}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{37}}{2*-1}=\frac{-20+2\sqrt{37}}{-2}
$