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(5n^2+24n+19)/2=6456
We move all terms to the left:
(5n^2+24n+19)/2-(6456)=0
We multiply all the terms by the denominator
(5n^2+24n+19)-6456*2=0
We add all the numbers together, and all the variables
(5n^2+24n+19)-12912=0
We get rid of parentheses
5n^2+24n+19-12912=0
We add all the numbers together, and all the variables
5n^2+24n-12893=0
a = 5; b = 24; c = -12893;
Δ = b2-4ac
Δ = 242-4·5·(-12893)
Δ = 258436
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{258436}=\sqrt{4*64609}=\sqrt{4}*\sqrt{64609}=2\sqrt{64609}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{64609}}{2*5}=\frac{-24-2\sqrt{64609}}{10} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{64609}}{2*5}=\frac{-24+2\sqrt{64609}}{10} $
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