Y=21+-1.5x^2

Solution for Y=21+-1.5x^2 equation:

=21+-1.5Y^2

We move all terms to the left:

-(21+-1.5Y^2)=0

We use the square of the difference formula

-(21-1.5Y^2)=0

We get rid of parentheses

1.5Y^2-21=0

a = 1.5; b = 0; c = -21;
Δ = b2-4ac
Δ = 02-4·1.5·(-21)
Δ = 126
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:

$\sqrt{\Delta}=\sqrt{126}=\sqrt{9*14}=\sqrt{9}*\sqrt{14}=3\sqrt{14}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{14}}{2*1.5}=\frac{0-3\sqrt{14}}{3}
=-\frac{3\sqrt{14}}{3}
=-\sqrt{14}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{14}}{2*1.5}=\frac{0+3\sqrt{14}}{3}
=\frac{3\sqrt{14}}{3}
=\sqrt{14}
$