x^2+11x-3=-2

Solution for x^2+11x-3=-2 equation:

x^2+11x-3=-2

We move all terms to the left:

x^2+11x-3-(-2)=0

We add all the numbers together, and all the variables

x^2+11x-1=0

a = 1; b = 11; c = -1;
Δ = b2-4ac
Δ = 112-4·1·(-1)
Δ = 125
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:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-5\sqrt{5}}{2*1}=\frac{-11-5\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+5\sqrt{5}}{2*1}=\frac{-11+5\sqrt{5}}{2}
$