25n+15n2=6500

Solution for 25n+15n2=6500 equation:

25n+15n^2=6500

We move all terms to the left:

25n+15n^2-(6500)=0

a = 15; b = 25; c = -6500;
Δ = b2-4ac
Δ = 252-4·15·(-6500)
Δ = 390625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{390625}=625$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-625}{2*15}=\frac{-650}{30}
=-21+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+625}{2*15}=\frac{600}{30}
=20
$