250=5x+x^2

Solution for 250=5x+x^2 equation:

250=5x+x^2

We move all terms to the left:

250-(5x+x^2)=0

We get rid of parentheses

-x^2-5x+250=0

We add all the numbers together, and all the variables

-1x^2-5x+250=0

a = -1; b = -5; c = +250;
Δ = b2-4ac
Δ = -52-4·(-1)·250
Δ = 1025
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:

$\sqrt{\Delta}=\sqrt{1025}=\sqrt{25*41}=\sqrt{25}*\sqrt{41}=5\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{41}}{2*-1}=\frac{5-5\sqrt{41}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{41}}{2*-1}=\frac{5+5\sqrt{41}}{-2}
$