9=((21)2-r2)

Solution for 9=((21)2-r2) equation:

9=((21)2-r2)

We move all terms to the left:

9-(((21)2-r2))=0

We add all the numbers together, and all the variables

-((-1r^2+212))+9=0


We calculate terms in parentheses: -((-1r^2+212)), so:

(-1r^2+212)

We get rid of parentheses

-1r^2+212

Back to the equation:

-(-1r^2+212)


We get rid of parentheses

1r^2-212+9=0

We add all the numbers together, and all the variables

r^2-203=0

a = 1; b = 0; c = -203;
Δ = b2-4ac
Δ = 02-4·1·(-203)
Δ = 812
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{812}=\sqrt{4*203}=\sqrt{4}*\sqrt{203}=2\sqrt{203}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{203}}{2*1}=\frac{0-2\sqrt{203}}{2}
=-\frac{2\sqrt{203}}{2}
=-\sqrt{203}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{203}}{2*1}=\frac{0+2\sqrt{203}}{2}
=\frac{2\sqrt{203}}{2}
=\sqrt{203}
$