x2-8x-19=0

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

x2-8x-19=0

We add all the numbers together, and all the variables

x^2-8x-19=0

a = 1; b = -8; c = -19;
Δ = b2-4ac
Δ = -82-4·1·(-19)
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{35}}{2*1}=\frac{8-2\sqrt{35}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{35}}{2*1}=\frac{8+2\sqrt{35}}{2}
$