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189=n2
We move all terms to the left:
189-(n2)=0
We add all the numbers together, and all the variables
-1n^2+189=0
a = -1; b = 0; c = +189;
Δ = b2-4ac
Δ = 02-4·(-1)·189
Δ = 756
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{21}}{2*-1}=\frac{0-6\sqrt{21}}{-2} =-\frac{6\sqrt{21}}{-2} =-\frac{3\sqrt{21}}{-1} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{21}}{2*-1}=\frac{0+6\sqrt{21}}{-2} =\frac{6\sqrt{21}}{-2} =\frac{3\sqrt{21}}{-1} $
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