19x2-12x-8=0

Solution for 19x2-12x-8=0 equation:

19x^2-12x-8=0

a = 19; b = -12; c = -8;
Δ = b2-4ac
Δ = -122-4·19·(-8)
Δ = 752
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:

$\sqrt{\Delta}=\sqrt{752}=\sqrt{16*47}=\sqrt{16}*\sqrt{47}=4\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{47}}{2*19}=\frac{12-4\sqrt{47}}{38}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{47}}{2*19}=\frac{12+4\sqrt{47}}{38}
$