11x+x^2=102

Solution for 11x+x^2=102 equation:

11x+x^2=102

We move all terms to the left:

11x+x^2-(102)=0

a = 1; b = 11; c = -102;
Δ = b2-4ac
Δ = 112-4·1·(-102)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-23}{2*1}=\frac{-34}{2}
=-17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+23}{2*1}=\frac{12}{2}
=6
$