X2+19x+24=396

Solution for X2+19x+24=396 equation:

X2+19X+24=396

We move all terms to the left:

X2+19X+24-(396)=0

We add all the numbers together, and all the variables

X^2+19X-372=0

a = 1; b = 19; c = -372;
Δ = b2-4ac
Δ = 192-4·1·(-372)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-43}{2*1}=\frac{-62}{2}
=-31
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+43}{2*1}=\frac{24}{2}
=12
$