10n^2+2=562

Solution for 10n^2+2=562 equation:

10n^2+2=562

We move all terms to the left:

10n^2+2-(562)=0

We add all the numbers together, and all the variables

10n^2-560=0

a = 10; b = 0; c = -560;
Δ = b2-4ac
Δ = 02-4·10·(-560)
Δ = 22400
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:

$\sqrt{\Delta}=\sqrt{22400}=\sqrt{1600*14}=\sqrt{1600}*\sqrt{14}=40\sqrt{14}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{14}}{2*10}=\frac{0-40\sqrt{14}}{20}
=-\frac{40\sqrt{14}}{20}
=-2\sqrt{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{14}}{2*10}=\frac{0+40\sqrt{14}}{20}
=\frac{40\sqrt{14}}{20}
=2\sqrt{14}
$