Y2-x2/80=0

Solution for Y2-x2/80=0 equation:

2-Y2/80=0

We multiply all the terms by the denominator


-Y2+2*80=0

We add all the numbers together, and all the variables

-1Y^2+160=0

a = -1; b = 0; c = +160;
Δ = b2-4ac
Δ = 02-4·(-1)·160
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{10}}{2*-1}=\frac{0-8\sqrt{10}}{-2}
=-\frac{8\sqrt{10}}{-2}
=-\frac{4\sqrt{10}}{-1}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{10}}{2*-1}=\frac{0+8\sqrt{10}}{-2}
=\frac{8\sqrt{10}}{-2}
=\frac{4\sqrt{10}}{-1}
$