x^2-x=1900

Solution for x^2-x=1900 equation:

x^2-x=1900

We move all terms to the left:

x^2-x-(1900)=0

We add all the numbers together, and all the variables

x^2-1x-1900=0

a = 1; b = -1; c = -1900;
Δ = b2-4ac
Δ = -12-4·1·(-1900)
Δ = 7601
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{7601}}{2*1}=\frac{1-\sqrt{7601}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{7601}}{2*1}=\frac{1+\sqrt{7601}}{2}
$