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n2-14n+38=0
We add all the numbers together, and all the variables
n^2-14n+38=0
a = 1; b = -14; c = +38;
Δ = b2-4ac
Δ = -142-4·1·38
Δ = 44
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{11}}{2*1}=\frac{14-2\sqrt{11}}{2} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{11}}{2*1}=\frac{14+2\sqrt{11}}{2} $
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