(x^2-x)/2=10000

Solution for (x^2-x)/2=10000 equation:

(x^2-x)/2=10000

We move all terms to the left:

(x^2-x)/2-(10000)=0

We multiply all the terms by the denominator


(x^2-x)-10000*2=0

We add all the numbers together, and all the variables

(x^2-x)-20000=0

We get rid of parentheses

x^2-x-20000=0

We add all the numbers together, and all the variables

x^2-1x-20000=0

a = 1; b = -1; c = -20000;
Δ = b2-4ac
Δ = -12-4·1·(-20000)
Δ = 80001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{80001}=\sqrt{9*8889}=\sqrt{9}*\sqrt{8889}=3\sqrt{8889}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3\sqrt{8889}}{2*1}=\frac{1-3\sqrt{8889}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{8889}}{2*1}=\frac{1+3\sqrt{8889}}{2}
$