19-x^2=-24

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

19-x^2=-24

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1x^2+43=0

a = -1; b = 0; c = +43;
Δ = b2-4ac
Δ = 02-4·(-1)·43
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{43}}{2*-1}=\frac{0-2\sqrt{43}}{-2}
=-\frac{2\sqrt{43}}{-2}
=-\frac{\sqrt{43}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{43}}{2*-1}=\frac{0+2\sqrt{43}}{-2}
=\frac{2\sqrt{43}}{-2}
=\frac{\sqrt{43}}{-1}
$