Y^2=10^2-x^2

Solution for Y^2=10^2-x^2 equation:

^2=10^2-Y^2

We move all terms to the left:

^2-(10^2-Y^2)=0

We add all the numbers together, and all the variables

-(10^2-Y^2)=0

We get rid of parentheses

Y^2-10^2=0

We add all the numbers together, and all the variables

Y^2-100=0

a = 1; b = 0; c = -100;
Δ = b2-4ac
Δ = 02-4·1·(-100)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20}{2*1}=\frac{-20}{2}
=-10
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20}{2*1}=\frac{20}{2}
=10
$