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180n^2=369=
We move all terms to the left:
180n^2-(369)=0
a = 180; b = 0; c = -369;
Δ = b2-4ac
Δ = 02-4·180·(-369)
Δ = 265680
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{265680}=\sqrt{1296*205}=\sqrt{1296}*\sqrt{205}=36\sqrt{205}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{205}}{2*180}=\frac{0-36\sqrt{205}}{360} =-\frac{36\sqrt{205}}{360} =-\frac{\sqrt{205}}{10} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{205}}{2*180}=\frac{0+36\sqrt{205}}{360} =\frac{36\sqrt{205}}{360} =\frac{\sqrt{205}}{10} $
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