x^2+18x-19=-4

Solution for x^2+18x-19=-4 equation:

x^2+18x-19=-4

We move all terms to the left:

x^2+18x-19-(-4)=0

We add all the numbers together, and all the variables

x^2+18x-15=0

a = 1; b = 18; c = -15;
Δ = b2-4ac
Δ = 182-4·1·(-15)
Δ = 384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-8\sqrt{6}}{2*1}=\frac{-18-8\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+8\sqrt{6}}{2*1}=\frac{-18+8\sqrt{6}}{2}
$