y^2-455=20976

Solution for y^2-455=20976 equation:

y^2-455=20976

We move all terms to the left:

y^2-455-(20976)=0

We add all the numbers together, and all the variables

y^2-21431=0

a = 1; b = 0; c = -21431;
Δ = b2-4ac
Δ = 02-4·1·(-21431)
Δ = 85724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{85724}=\sqrt{4*21431}=\sqrt{4}*\sqrt{21431}=2\sqrt{21431}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{21431}}{2*1}=\frac{0-2\sqrt{21431}}{2}
=-\frac{2\sqrt{21431}}{2}
=-\sqrt{21431}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{21431}}{2*1}=\frac{0+2\sqrt{21431}}{2}
=\frac{2\sqrt{21431}}{2}
=\sqrt{21431}
$