x^2-x=812

Solution for x^2-x=812 equation:

x^2-x=812

We move all terms to the left:

x^2-x-(812)=0

We add all the numbers together, and all the variables

x^2-1x-812=0

a = 1; b = -1; c = -812;
Δ = b2-4ac
Δ = -12-4·1·(-812)
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-57}{2*1}=\frac{-56}{2}
=-28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+57}{2*1}=\frac{58}{2}
=29
$