500+30(n-3)=350+45(n-5)n=

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Solution for 500+30(n-3)=350+45(n-5)n= equation:



500+30(n-3)=350+45(n-5)n=
We move all terms to the left:
500+30(n-3)-(350+45(n-5)n)=0
We multiply parentheses
30n-(350+45(n-5)n)-90+500=0
We calculate terms in parentheses: -(350+45(n-5)n), so:
350+45(n-5)n
determiningTheFunctionDomain 45(n-5)n+350
We multiply parentheses
45n^2-225n+350
Back to the equation:
-(45n^2-225n+350)
We add all the numbers together, and all the variables
30n-(45n^2-225n+350)+410=0
We get rid of parentheses
-45n^2+30n+225n-350+410=0
We add all the numbers together, and all the variables
-45n^2+255n+60=0
a = -45; b = 255; c = +60;
Δ = b2-4ac
Δ = 2552-4·(-45)·60
Δ = 75825
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:
$\sqrt{\Delta}=\sqrt{75825}=\sqrt{225*337}=\sqrt{225}*\sqrt{337}=15\sqrt{337}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(255)-15\sqrt{337}}{2*-45}=\frac{-255-15\sqrt{337}}{-90} $
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(255)+15\sqrt{337}}{2*-45}=\frac{-255+15\sqrt{337}}{-90} $

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