19x^2+11x+1=0

Solution for 19x^2+11x+1=0 equation:

19x^2+11x+1=0

a = 19; b = 11; c = +1;
Δ = b2-4ac
Δ = 112-4·19·1
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-3\sqrt{5}}{2*19}=\frac{-11-3\sqrt{5}}{38}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+3\sqrt{5}}{2*19}=\frac{-11+3\sqrt{5}}{38}
$