3-10n^2=-957

Solution for 3-10n^2=-957 equation:

3-10n^2=-957

We move all terms to the left:

3-10n^2-(-957)=0

We add all the numbers together, and all the variables

-10n^2+960=0

a = -10; b = 0; c = +960;
Δ = b2-4ac
Δ = 02-4·(-10)·960
Δ = 38400
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:

$\sqrt{\Delta}=\sqrt{38400}=\sqrt{6400*6}=\sqrt{6400}*\sqrt{6}=80\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{6}}{2*-10}=\frac{0-80\sqrt{6}}{-20}
=-\frac{80\sqrt{6}}{-20}
=-\frac{4\sqrt{6}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{6}}{2*-10}=\frac{0+80\sqrt{6}}{-20}
=\frac{80\sqrt{6}}{-20}
=\frac{4\sqrt{6}}{-1}
$