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n-2/n*180=172
We move all terms to the left:
n-2/n*180-(172)=0
Domain of the equation: n*180!=0We multiply all the terms by the denominator
n!=0/1
n!=0
n∈R
n*n*180-172*n*180-2=0
Wy multiply elements
180n^2*1-30960n*1-2=0
Wy multiply elements
180n^2-30960n-2=0
a = 180; b = -30960; c = -2;
Δ = b2-4ac
Δ = -309602-4·180·(-2)
Δ = 958523040
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{958523040}=\sqrt{144*6656410}=\sqrt{144}*\sqrt{6656410}=12\sqrt{6656410}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30960)-12\sqrt{6656410}}{2*180}=\frac{30960-12\sqrt{6656410}}{360} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30960)+12\sqrt{6656410}}{2*180}=\frac{30960+12\sqrt{6656410}}{360} $
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