10n+5=20n^2

Solution for 10n+5=20n^2 equation:

10n+5=20n^2

We move all terms to the left:

10n+5-(20n^2)=0

determiningTheFunctionDomain
-20n^2+10n+5=0

a = -20; b = 10; c = +5;
Δ = b2-4ac
Δ = 102-4·(-20)·5
Δ = 500
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:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{5}}{2*-20}=\frac{-10-10\sqrt{5}}{-40}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{5}}{2*-20}=\frac{-10+10\sqrt{5}}{-40}
$