((X^2-x)/2)=666

Solution for ((X^2-x)/2)=666 equation:

((X^2-X)/2)=666

We move all terms to the left:

((X^2-X)/2)-(666)=0

We multiply all the terms by the denominator


((X^2-X)-666*2)=0


We calculate terms in parentheses: +((X^2-X)-666*2), so:

(X^2-X)-666*2

We add all the numbers together, and all the variables

(X^2-X)-1332

We get rid of parentheses

X^2-X-1332

We add all the numbers together, and all the variables

X^2-1X-1332

Back to the equation:

+(X^2-1X-1332)


We get rid of parentheses

X^2-1X-1332=0

a = 1; b = -1; c = -1332;
Δ = b2-4ac
Δ = -12-4·1·(-1332)
Δ = 5329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5329}=73$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-73}{2*1}=\frac{-72}{2}
=-36
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+73}{2*1}=\frac{74}{2}
=37
$