x^2+x+250=2800

Solution for x^2+x+250=2800 equation:

x^2+x+250=2800

We move all terms to the left:

x^2+x+250-(2800)=0

We add all the numbers together, and all the variables

x^2+x-2550=0

a = 1; b = 1; c = -2550;
Δ = b2-4ac
Δ = 12-4·1·(-2550)
Δ = 10201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10201}=101$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-101}{2*1}=\frac{-102}{2}
=-51
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+101}{2*1}=\frac{100}{2}
=50
$