11x+x^2=126

Solution for 11x+x^2=126 equation:

11x+x^2=126

We move all terms to the left:

11x+x^2-(126)=0

a = 1; b = 11; c = -126;
Δ = b2-4ac
Δ = 112-4·1·(-126)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-25}{2*1}=\frac{-36}{2}
=-18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+25}{2*1}=\frac{14}{2}
=7
$