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6n^2+12n-23=0
a = 6; b = 12; c = -23;
Δ = b2-4ac
Δ = 122-4·6·(-23)
Δ = 696
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{696}=\sqrt{4*174}=\sqrt{4}*\sqrt{174}=2\sqrt{174}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{174}}{2*6}=\frac{-12-2\sqrt{174}}{12} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{174}}{2*6}=\frac{-12+2\sqrt{174}}{12} $
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