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5n+5n(3n+10)=525
We move all terms to the left:
5n+5n(3n+10)-(525)=0
We multiply parentheses
15n^2+5n+50n-525=0
We add all the numbers together, and all the variables
15n^2+55n-525=0
a = 15; b = 55; c = -525;
Δ = b2-4ac
Δ = 552-4·15·(-525)
Δ = 34525
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{34525}=\sqrt{25*1381}=\sqrt{25}*\sqrt{1381}=5\sqrt{1381}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-5\sqrt{1381}}{2*15}=\frac{-55-5\sqrt{1381}}{30} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+5\sqrt{1381}}{2*15}=\frac{-55+5\sqrt{1381}}{30} $
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