r2=199

Solution for r2=199 equation:

r2=199

We move all terms to the left:

r2-(199)=0

We add all the numbers together, and all the variables

r^2-199=0

a = 1; b = 0; c = -199;
Δ = b2-4ac
Δ = 02-4·1·(-199)
Δ = 796
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:

$\sqrt{\Delta}=\sqrt{796}=\sqrt{4*199}=\sqrt{4}*\sqrt{199}=2\sqrt{199}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{199}}{2*1}=\frac{0-2\sqrt{199}}{2}
=-\frac{2\sqrt{199}}{2}
=-\sqrt{199}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{199}}{2*1}=\frac{0+2\sqrt{199}}{2}
=\frac{2\sqrt{199}}{2}
=\sqrt{199}
$