x^2=-11x-17

Solution for x^2=-11x-17 equation:

x^2=-11x-17

We move all terms to the left:

x^2-(-11x-17)=0

We get rid of parentheses

x^2+11x+17=0

a = 1; b = 11; c = +17;
Δ = b2-4ac
Δ = 112-4·1·17
Δ = 53
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{53}}{2*1}=\frac{-11-\sqrt{53}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{53}}{2*1}=\frac{-11+\sqrt{53}}{2}
$