Y=162-8x^2

Solution for Y=162-8x^2 equation:

=162-8Y^2

We move all terms to the left:

-(162-8Y^2)=0

We get rid of parentheses

8Y^2-162=0

a = 8; b = 0; c = -162;
Δ = b2-4ac
Δ = 02-4·8·(-162)
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72}{2*8}=\frac{-72}{16}
=-4+1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72}{2*8}=\frac{72}{16}
=4+1/2
$