(x^2)-x=333

Solution for (x^2)-x=333 equation:

(x^2)-x=333

We move all terms to the left:

(x^2)-x-(333)=0

We add all the numbers together, and all the variables

x^2-1x-333=0

a = 1; b = -1; c = -333;
Δ = b2-4ac
Δ = -12-4·1·(-333)
Δ = 1333
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{1333}}{2*1}=\frac{1-\sqrt{1333}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1333}}{2*1}=\frac{1+\sqrt{1333}}{2}
$