5n^2=10n+10=0

Solution for 5n^2=10n+10=0 equation:

5n^2=10n+10=0

We move all terms to the left:

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

We get rid of parentheses

5n^2-10n-10=0

a = 5; b = -10; c = -10;
Δ = b2-4ac
Δ = -102-4·5·(-10)
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{3}}{2*5}=\frac{10-10\sqrt{3}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{3}}{2*5}=\frac{10+10\sqrt{3}}{10}
$