Y=15-25x^2

Solution for Y=15-25x^2 equation:

=15-25Y^2

We move all terms to the left:

-(15-25Y^2)=0

We get rid of parentheses

25Y^2-15=0

a = 25; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·25·(-15)
Δ = 1500
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:

$\sqrt{\Delta}=\sqrt{1500}=\sqrt{100*15}=\sqrt{100}*\sqrt{15}=10\sqrt{15}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{15}}{2*25}=\frac{0-10\sqrt{15}}{50}
=-\frac{10\sqrt{15}}{50}
=-\frac{\sqrt{15}}{5}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{15}}{2*25}=\frac{0+10\sqrt{15}}{50}
=\frac{10\sqrt{15}}{50}
=\frac{\sqrt{15}}{5}
$