x^2+16x=11

Solution for x^2+16x=11 equation:

x^2+16x=11

We move all terms to the left:

x^2+16x-(11)=0

a = 1; b = 16; c = -11;
Δ = b2-4ac
Δ = 162-4·1·(-11)
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-10\sqrt{3}}{2*1}=\frac{-16-10\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+10\sqrt{3}}{2*1}=\frac{-16+10\sqrt{3}}{2}
$