10n2-10=470

Solution for 10n2-10=470 equation:

10n^2-10=470

We move all terms to the left:

10n^2-10-(470)=0

We add all the numbers together, and all the variables

10n^2-480=0

a = 10; b = 0; c = -480;
Δ = b2-4ac
Δ = 02-4·10·(-480)
Δ = 19200
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:

$\sqrt{\Delta}=\sqrt{19200}=\sqrt{6400*3}=\sqrt{6400}*\sqrt{3}=80\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{3}}{2*10}=\frac{0-80\sqrt{3}}{20}
=-\frac{80\sqrt{3}}{20}
=-4\sqrt{3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{3}}{2*10}=\frac{0+80\sqrt{3}}{20}
=\frac{80\sqrt{3}}{20}
=4\sqrt{3}
$