x^2+19=4-8x

Solution for x^2+19=4-8x equation:

x^2+19=4-8x

We move all terms to the left:

x^2+19-(4-8x)=0

We add all the numbers together, and all the variables

x^2-(-8x+4)+19=0

We get rid of parentheses

x^2+8x-4+19=0

We add all the numbers together, and all the variables

x^2+8x+15=0

a = 1; b = 8; c = +15;
Δ = b2-4ac
Δ = 82-4·1·15
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2}{2*1}=\frac{-6}{2}
=-3
$