x^2+24x+19=-15

Solution for x^2+24x+19=-15 equation:

x^2+24x+19=-15

We move all terms to the left:

x^2+24x+19-(-15)=0

We add all the numbers together, and all the variables

x^2+24x+34=0

a = 1; b = 24; c = +34;
Δ = b2-4ac
Δ = 242-4·1·34
Δ = 440
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:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{110}}{2*1}=\frac{-24-2\sqrt{110}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{110}}{2*1}=\frac{-24+2\sqrt{110}}{2}
$