5n+7n^2=10

Solution for 5n+7n^2=10 equation:

5n+7n^2=10

We move all terms to the left:

5n+7n^2-(10)=0

a = 7; b = 5; c = -10;
Δ = b2-4ac
Δ = 52-4·7·(-10)
Δ = 305
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{305}}{2*7}=\frac{-5-\sqrt{305}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{305}}{2*7}=\frac{-5+\sqrt{305}}{14}
$