Y=6x^2-900

Solution for Y=6x^2-900 equation:

=6Y^2-900

We move all terms to the left:

-(6Y^2-900)=0

We get rid of parentheses

-6Y^2+900=0

a = -6; b = 0; c = +900;
Δ = b2-4ac
Δ = 02-4·(-6)·900
Δ = 21600
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:

$\sqrt{\Delta}=\sqrt{21600}=\sqrt{3600*6}=\sqrt{3600}*\sqrt{6}=60\sqrt{6}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{6}}{2*-6}=\frac{0-60\sqrt{6}}{-12}
=-\frac{60\sqrt{6}}{-12}
=-\frac{5\sqrt{6}}{-1}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{6}}{2*-6}=\frac{0+60\sqrt{6}}{-12}
=\frac{60\sqrt{6}}{-12}
=\frac{5\sqrt{6}}{-1}
$