x^2+11x-18=1

Solution for x^2+11x-18=1 equation:

x^2+11x-18=1

We move all terms to the left:

x^2+11x-18-(1)=0

We add all the numbers together, and all the variables

x^2+11x-19=0

a = 1; b = 11; c = -19;
Δ = b2-4ac
Δ = 112-4·1·(-19)
Δ = 197
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{197}}{2*1}=\frac{-11-\sqrt{197}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{197}}{2*1}=\frac{-11+\sqrt{197}}{2}
$