11x+x^2=121

Solution for 11x+x^2=121 equation:

11x+x^2=121

We move all terms to the left:

11x+x^2-(121)=0

a = 1; b = 11; c = -121;
Δ = b2-4ac
Δ = 112-4·1·(-121)
Δ = 605
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:

$\sqrt{\Delta}=\sqrt{605}=\sqrt{121*5}=\sqrt{121}*\sqrt{5}=11\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11\sqrt{5}}{2*1}=\frac{-11-11\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11\sqrt{5}}{2*1}=\frac{-11+11\sqrt{5}}{2}
$