19x^2-42x-20=0

Solution for 19x^2-42x-20=0 equation:

19x^2-42x-20=0

a = 19; b = -42; c = -20;
Δ = b2-4ac
Δ = -422-4·19·(-20)
Δ = 3284
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:

$\sqrt{\Delta}=\sqrt{3284}=\sqrt{4*821}=\sqrt{4}*\sqrt{821}=2\sqrt{821}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{821}}{2*19}=\frac{42-2\sqrt{821}}{38}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{821}}{2*19}=\frac{42+2\sqrt{821}}{38}
$