0=8x^2+19x

Solution for 0=8x^2+19x equation:

0=8x^2+19x

We move all terms to the left:

0-(8x^2+19x)=0

We add all the numbers together, and all the variables

-(8x^2+19x)=0

We get rid of parentheses

-8x^2-19x=0

a = -8; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·(-8)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*-8}=\frac{0}{-16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*-8}=\frac{38}{-16}
=-2+3/8
$