2x^2-x=10000

Solution for 2x^2-x=10000 equation:

2x^2-x=10000

We move all terms to the left:

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

We add all the numbers together, and all the variables

2x^2-1x-10000=0

a = 2; b = -1; c = -10000;
Δ = b2-4ac
Δ = -12-4·2·(-10000)
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*2}=\frac{1-3\sqrt{8889}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{8889}}{2*2}=\frac{1+3\sqrt{8889}}{4}
$