-4=2x^2+3x-19

Solution for -4=2x^2+3x-19 equation:

-4=2x^2+3x-19

We move all terms to the left:

-4-(2x^2+3x-19)=0

We get rid of parentheses

-2x^2-3x+19-4=0

We add all the numbers together, and all the variables

-2x^2-3x+15=0

a = -2; b = -3; c = +15;
Δ = b2-4ac
Δ = -32-4·(-2)·15
Δ = 129
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{-(-3)-\sqrt{129}}{2*-2}=\frac{3-\sqrt{129}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{129}}{2*-2}=\frac{3+\sqrt{129}}{-4}
$