X+x^2+9x=250

Solution for X+x^2+9x=250 equation:

X+X^2+9X=250

We move all terms to the left:

X+X^2+9X-(250)=0

We add all the numbers together, and all the variables

X^2+10X-250=0

a = 1; b = 10; c = -250;
Δ = b2-4ac
Δ = 102-4·1·(-250)
Δ = 1100
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:

$\sqrt{\Delta}=\sqrt{1100}=\sqrt{100*11}=\sqrt{100}*\sqrt{11}=10\sqrt{11}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{11}}{2*1}=\frac{-10-10\sqrt{11}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{11}}{2*1}=\frac{-10+10\sqrt{11}}{2}
$