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19-3n+25/nn=5
We move all terms to the left:
19-3n+25/nn-(5)=0
Domain of the equation: nn!=0We add all the numbers together, and all the variables
n!=0/1
n!=0
n∈R
-3n+25/nn+14=0
We multiply all the terms by the denominator
-3n*nn+14*nn+25=0
Wy multiply elements
-3n^2+14n+25=0
a = -3; b = 14; c = +25;
Δ = b2-4ac
Δ = 142-4·(-3)·25
Δ = 496
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4\sqrt{31}}{2*-3}=\frac{-14-4\sqrt{31}}{-6} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4\sqrt{31}}{2*-3}=\frac{-14+4\sqrt{31}}{-6} $
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