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(5n+15)(3n+29)=180
We move all terms to the left:
(5n+15)(3n+29)-(180)=0
We multiply parentheses ..
(+15n^2+145n+45n+435)-180=0
We get rid of parentheses
15n^2+145n+45n+435-180=0
We add all the numbers together, and all the variables
15n^2+190n+255=0
a = 15; b = 190; c = +255;
Δ = b2-4ac
Δ = 1902-4·15·255
Δ = 20800
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20800}=\sqrt{1600*13}=\sqrt{1600}*\sqrt{13}=40\sqrt{13}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(190)-40\sqrt{13}}{2*15}=\frac{-190-40\sqrt{13}}{30} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(190)+40\sqrt{13}}{2*15}=\frac{-190+40\sqrt{13}}{30} $
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