5n+3n^2=375

Solution for 5n+3n^2=375 equation:

5n+3n^2=375

We move all terms to the left:

5n+3n^2-(375)=0

a = 3; b = 5; c = -375;
Δ = b2-4ac
Δ = 52-4·3·(-375)
Δ = 4525
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:

$\sqrt{\Delta}=\sqrt{4525}=\sqrt{25*181}=\sqrt{25}*\sqrt{181}=5\sqrt{181}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{181}}{2*3}=\frac{-5-5\sqrt{181}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{181}}{2*3}=\frac{-5+5\sqrt{181}}{6}
$