Y=1/4x^2-1-8

Solution for Y=1/4x^2-1-8 equation:

=1/4Y^2-1-8

We move all terms to the left:

-(1/4Y^2-1-8)=0


Domain of the equation: 4Y^2-1-8)!=0

We move all terms containing Y to the left, all other terms to the right

4Y^2-8)!=1

Y∈R


We get rid of parentheses

-1/4Y^2+1+8=0

We multiply all the terms by the denominator


1*4Y^2+8*4Y^2-1=0

Wy multiply elements

4Y^2+32Y^2-1=0

We add all the numbers together, and all the variables

36Y^2-1=0

a = 36; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·36·(-1)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*36}=\frac{-12}{72}
=-1/6
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*36}=\frac{12}{72}
=1/6
$