x^2+16x-2=11

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

x^2+16x-2=11

We move all terms to the left:

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

We add all the numbers together, and all the variables

x^2+16x-13=0

a = 1; b = 16; c = -13;
Δ = b2-4ac
Δ = 162-4·1·(-13)
Δ = 308
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:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{77}}{2*1}=\frac{-16-2\sqrt{77}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{77}}{2*1}=\frac{-16+2\sqrt{77}}{2}
$