6x^2+19x=-8

Solution for 6x^2+19x=-8 equation:

6x^2+19x=-8

We move all terms to the left:

6x^2+19x-(-8)=0

We add all the numbers together, and all the variables

6x^2+19x+8=0

a = 6; b = 19; c = +8;
Δ = b2-4ac
Δ = 192-4·6·8
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-13}{2*6}=\frac{-32}{12}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+13}{2*6}=\frac{-6}{12}
=-1/2
$