r^2=194

Solution for r^2=194 equation:

r^2=194

We move all terms to the left:

r^2-(194)=0

a = 1; b = 0; c = -194;
Δ = b2-4ac
Δ = 02-4·1·(-194)
Δ = 776
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:

$\sqrt{\Delta}=\sqrt{776}=\sqrt{4*194}=\sqrt{4}*\sqrt{194}=2\sqrt{194}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{194}}{2*1}=\frac{0-2\sqrt{194}}{2}
=-\frac{2\sqrt{194}}{2}
=-\sqrt{194}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{194}}{2*1}=\frac{0+2\sqrt{194}}{2}
=\frac{2\sqrt{194}}{2}
=\sqrt{194}
$