x^2+x-19.1844=0

Solution for x^2+x-19.1844=0 equation:

x^2+x-19.1844=0

a = 1; b = 1; c = -19.1844;
Δ = b2-4ac
Δ = 12-4·1·(-19.1844)
Δ = 77.7376
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{-(1)-\sqrt{77.7376}}{2*1}=\frac{-1-\sqrt{77.7376}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{77.7376}}{2*1}=\frac{-1+\sqrt{77.7376}}{2}
$