Y=(x2-2)500

Solution for Y=(x2-2)500 equation:

=(Y2-2)500

We move all terms to the left:

-((Y2-2)500)=0

We add all the numbers together, and all the variables

-((+Y^2-2)500)=0


We calculate terms in parentheses: -((+Y^2-2)500), so:

(+Y^2-2)500

We multiply parentheses

500Y^2-1000

Back to the equation:

-(500Y^2-1000)


We get rid of parentheses

-500Y^2+1000=0

a = -500; b = 0; c = +1000;
Δ = b2-4ac
Δ = 02-4·(-500)·1000
Δ = 2000000
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:

$\sqrt{\Delta}=\sqrt{2000000}=\sqrt{1000000*2}=\sqrt{1000000}*\sqrt{2}=1000\sqrt{2}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1000\sqrt{2}}{2*-500}=\frac{0-1000\sqrt{2}}{-1000}
=-\frac{1000\sqrt{2}}{-1000}
=-\frac{\sqrt{2}}{-1}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1000\sqrt{2}}{2*-500}=\frac{0+1000\sqrt{2}}{-1000}
=\frac{1000\sqrt{2}}{-1000}
=\frac{\sqrt{2}}{-1}
$