Y=100-225x^2

Solution for Y=100-225x^2 equation:

=100-225Y^2

We move all terms to the left:

-(100-225Y^2)=0

We get rid of parentheses

225Y^2-100=0

a = 225; b = 0; c = -100;
Δ = b2-4ac
Δ = 02-4·225·(-100)
Δ = 90000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{90000}=300$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-300}{2*225}=\frac{-300}{450}
=-2/3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+300}{2*225}=\frac{300}{450}
=2/3
$