0=3x^2+5x-19

Solution for 0=3x^2+5x-19 equation:

0=3x^2+5x-19

We move all terms to the left:

0-(3x^2+5x-19)=0

We add all the numbers together, and all the variables

-(3x^2+5x-19)=0

We get rid of parentheses

-3x^2-5x+19=0

a = -3; b = -5; c = +19;
Δ = b2-4ac
Δ = -52-4·(-3)·19
Δ = 253
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{253}}{2*-3}=\frac{5-\sqrt{253}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{253}}{2*-3}=\frac{5+\sqrt{253}}{-6}
$