10n^2=-62n+14

Solution for 10n^2=-62n+14 equation:

10n^2=-62n+14

We move all terms to the left:

10n^2-(-62n+14)=0

We get rid of parentheses

10n^2+62n-14=0

a = 10; b = 62; c = -14;
Δ = b2-4ac
Δ = 622-4·10·(-14)
Δ = 4404
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:

$\sqrt{\Delta}=\sqrt{4404}=\sqrt{4*1101}=\sqrt{4}*\sqrt{1101}=2\sqrt{1101}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-2\sqrt{1101}}{2*10}=\frac{-62-2\sqrt{1101}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+2\sqrt{1101}}{2*10}=\frac{-62+2\sqrt{1101}}{20}
$