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-6n^2=-138
We move all terms to the left:
-6n^2-(-138)=0
We add all the numbers together, and all the variables
-6n^2+138=0
a = -6; b = 0; c = +138;
Δ = b2-4ac
Δ = 02-4·(-6)·138
Δ = 3312
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3312}=\sqrt{144*23}=\sqrt{144}*\sqrt{23}=12\sqrt{23}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{23}}{2*-6}=\frac{0-12\sqrt{23}}{-12} =-\frac{12\sqrt{23}}{-12} =-\frac{\sqrt{23}}{-1} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{23}}{2*-6}=\frac{0+12\sqrt{23}}{-12} =\frac{12\sqrt{23}}{-12} =\frac{\sqrt{23}}{-1} $
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