19x2+6x-3=0

Solution for 19x2+6x-3=0 equation:

19x^2+6x-3=0

a = 19; b = 6; c = -3;
Δ = b2-4ac
Δ = 62-4·19·(-3)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{66}}{2*19}=\frac{-6-2\sqrt{66}}{38}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{66}}{2*19}=\frac{-6+2\sqrt{66}}{38}
$