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2n(8+5n)-3=45
We move all terms to the left:
2n(8+5n)-3-(45)=0
We add all the numbers together, and all the variables
2n(5n+8)-3-45=0
We add all the numbers together, and all the variables
2n(5n+8)-48=0
We multiply parentheses
10n^2+16n-48=0
a = 10; b = 16; c = -48;
Δ = b2-4ac
Δ = 162-4·10·(-48)
Δ = 2176
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8\sqrt{34}}{2*10}=\frac{-16-8\sqrt{34}}{20} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8\sqrt{34}}{2*10}=\frac{-16+8\sqrt{34}}{20} $
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