X2+9x-11=0

Solution for X2+9x-11=0 equation:

X2+9X-11=0

We add all the numbers together, and all the variables

X^2+9X-11=0

a = 1; b = 9; c = -11;
Δ = b2-4ac
Δ = 92-4·1·(-11)
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{-(9)-5\sqrt{5}}{2*1}=\frac{-9-5\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+5\sqrt{5}}{2*1}=\frac{-9+5\sqrt{5}}{2}
$