-10n^2+7=6

Solution for -10n^2+7=6 equation:

-10n^2+7=6

We move all terms to the left:

-10n^2+7-(6)=0

We add all the numbers together, and all the variables

-10n^2+1=0

a = -10; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-10)·1
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{10}}{2*-10}=\frac{0-2\sqrt{10}}{-20}
=-\frac{2\sqrt{10}}{-20}
=-\frac{\sqrt{10}}{-10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{10}}{2*-10}=\frac{0+2\sqrt{10}}{-20}
=\frac{2\sqrt{10}}{-20}
=\frac{\sqrt{10}}{-10}
$