x^2+11(x)=82

Solution for x^2+11(x)=82 equation:

x^2+11(x)=82

We move all terms to the left:

x^2+11(x)-(82)=0

a = 1; b = 11; c = -82;
Δ = b2-4ac
Δ = 112-4·1·(-82)
Δ = 449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{449}}{2*1}=\frac{-11-\sqrt{449}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{449}}{2*1}=\frac{-11+\sqrt{449}}{2}
$