1-6n^2=-89

Solution for 1-6n^2=-89 equation:

1-6n^2=-89

We move all terms to the left:

1-6n^2-(-89)=0

We add all the numbers together, and all the variables

-6n^2+90=0

a = -6; b = 0; c = +90;
Δ = b2-4ac
Δ = 02-4·(-6)·90
Δ = 2160
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:

$\sqrt{\Delta}=\sqrt{2160}=\sqrt{144*15}=\sqrt{144}*\sqrt{15}=12\sqrt{15}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{15}}{2*-6}=\frac{0-12\sqrt{15}}{-12}
=-\frac{12\sqrt{15}}{-12}
=-\frac{\sqrt{15}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{15}}{2*-6}=\frac{0+12\sqrt{15}}{-12}
=\frac{12\sqrt{15}}{-12}
=\frac{\sqrt{15}}{-1}
$