-10-7n^2=-31

Solution for -10-7n^2=-31 equation:

-10-7n^2=-31

We move all terms to the left:

-10-7n^2-(-31)=0

We add all the numbers together, and all the variables

-7n^2+21=0

a = -7; b = 0; c = +21;
Δ = b2-4ac
Δ = 02-4·(-7)·21
Δ = 588
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:

$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{3}}{2*-7}=\frac{0-14\sqrt{3}}{-14}
=-\frac{14\sqrt{3}}{-14}
=-\frac{\sqrt{3}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{3}}{2*-7}=\frac{0+14\sqrt{3}}{-14}
=\frac{14\sqrt{3}}{-14}
=\frac{\sqrt{3}}{-1}
$