Y=1/2x^2-6

Solution for Y=1/2x^2-6 equation:

=1/2Y^2-6

We move all terms to the left:

-(1/2Y^2-6)=0


Domain of the equation: 2Y^2-6)!=0

Y∈R


We get rid of parentheses

-1/2Y^2+6=0

We multiply all the terms by the denominator


6*2Y^2-1=0

Wy multiply elements

12Y^2-1=0

a = 12; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·12·(-1)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*12}=\frac{0-4\sqrt{3}}{24}
=-\frac{4\sqrt{3}}{24}
=-\frac{\sqrt{3}}{6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*12}=\frac{0+4\sqrt{3}}{24}
=\frac{4\sqrt{3}}{24}
=\frac{\sqrt{3}}{6}
$